TY - GEN A1 - Li, Yongge A1 - Mei, Ruoxing A1 - Xu, Yong A1 - Kurths, Jürgen A1 - Duan, Jinqiao A1 - Metzler, Ralf T1 - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 974 KW - diffusion KW - channel KW - space-dependent diffusivity Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474542 SN - 1866-8372 IS - 974 ER - TY - JOUR A1 - Li, Yongge A1 - Mei, Ruoxing A1 - Xu, Yong A1 - Kurths, Jürgen A1 - Duan, Jinqiao A1 - Metzler, Ralf T1 - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity JF - New Journal of Physics N2 - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed. KW - diffusion KW - channel KW - space-dependent diffusivity Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/ab81b9 SN - 1367-2630 VL - 22 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - JOUR A1 - Agarwal, Ankit A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Öztürk, Ugur A1 - Kurths, Jürgen A1 - Merz, Bruno T1 - Optimal design of hydrometric station networks based on complex network analysis JF - Hydrology and Earth System Sciences N2 - Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure – the weighted degree–betweenness (WDB) measure – to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail. KW - identifying influential nodes KW - climate networks KW - rainfall KW - streamflow KW - synchronization KW - precipitation KW - classification KW - events Y1 - 2020 U6 - https://doi.org/10.5194/hess-24-2235-2020 SN - 1027-5606 SN - 1607-7938 VL - 24 IS - 5 SP - 2235 EP - 2251 PB - Copernicus Publ. CY - Göttingen ER - TY - GEN A1 - Agarwal, Ankit A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Öztürk, Ugur A1 - Kurths, Jürgen A1 - Merz, Bruno T1 - Optimal design of hydrometric station networks based on complex network analysis T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure – the weighted degree–betweenness (WDB) measure – to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 951 KW - identifying influential nodes KW - climate networks KW - rainfall KW - streamflow KW - synchronization KW - precipitation KW - classification KW - events Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471006 SN - 1866-8372 IS - 951 ER - TY - GEN A1 - Ciemer, Catrin A1 - Rehm, Lars A1 - Kurths, Jürgen A1 - Donner, Reik Volker A1 - Winkelmann, Ricarda A1 - Boers, Niklas T1 - An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1207 KW - complex networks KW - droughts KW - prediction KW - Amazon rainforest Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-525863 SN - 1866-8372 IS - 9 ER - TY - JOUR A1 - Ciemer, Catrin A1 - Rehm, Lars A1 - Kurths, Jürgen A1 - Donner, Reik Volker A1 - Winkelmann, Ricarda A1 - Boers, Niklas T1 - An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures JF - Environmental Research Letters N2 - Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months. KW - complex networks KW - droughts KW - prediction KW - Amazon rainforest Y1 - 2019 VL - 15 IS - 9 PB - IOP - Institute of Physics Publishing CY - Bristol ER - TY - JOUR A1 - Ozturk, Ugur A1 - Malik, Nishant A1 - Cheung, Kevin A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - A network-based comparative study of extreme tropical and frontal storm rainfall over Japan JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - Frequent and intense rainfall events demand innovative techniques to better predict the extreme rainfall dynamics. This task requires essentially the assessment of the basic types of atmospheric processes that trigger extreme rainfall, and then to examine the differences between those processes, which may help to identify key patterns to improve predictive algorithms. We employ tools from network theory to compare the spatial features of extreme rainfall over the Japanese archipelago and surrounding areas caused by two atmospheric processes: the Baiu front, which occurs mainly in June and July (JJ), and the tropical storms from August to November (ASON). We infer from complex networks of satellite-derived rainfall data, which are based on the nonlinear correlation measure of event synchronization. We compare the spatial scales involved in both systems and identify different regions which receive rainfall due to the large spatial scale of the Baiu and tropical storm systems. We observed that the spatial scales involved in the Baiu driven rainfall extremes, including the synoptic processes behind the frontal development, are larger than tropical storms, which even have long tracks during extratropical transitions. We further delineate regions of coherent rainfall during the two seasons based on network communities, identifying the horizontal (east-west) rainfall bands during JJ over the Japanese archipelago, while during ASON these bands align with the island arc of Japan. KW - Extreme rainfall KW - Baiu KW - Tropical storms KW - Event synchronization KW - Complex networks Y1 - 2019 U6 - https://doi.org/10.1007/s00382-018-4597-1 SN - 0930-7575 SN - 1432-0894 VL - 53 IS - 1-2 SP - 521 EP - 532 PB - Springer CY - New York ER - TY - JOUR A1 - Maheswaran, Rathinasamy A1 - Agarwal, Ankit A1 - Sivakumar, Bellie A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Wavelet analysis of precipitation extremes over India and teleconnections to climate indices JF - Stochastic Environmental Research and Risk Assessment N2 - Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Nino 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Nino 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region. KW - Extreme precipitation KW - Teleconnection patterns KW - Wavelets KW - Partial wavelet coherence KW - India Y1 - 2019 U6 - https://doi.org/10.1007/s00477-019-01738-3 SN - 1436-3240 SN - 1436-3259 VL - 33 IS - 11-12 SP - 2053 EP - 2069 PB - Springer CY - New York ER - TY - JOUR A1 - Boers, Niklas A1 - Goswami, Bedartha A1 - Rheinwalt, Aljoscha A1 - Bookhagen, Bodo A1 - Hoskins, Brian A1 - Kurths, Jürgen T1 - Complex networks reveal global pattern of extreme-rainfall teleconnections JF - Nature : the international weekly journal of science N2 - Climatic observables are often correlated across long spatial distances, and extreme events, such as heatwaves or floods, are typically assumed to be related to such teleconnections(1,2). Revealing atmospheric teleconnection patterns and understanding their underlying mechanisms is of great importance for weather forecasting in general and extreme-event prediction in particular(3,4), especially considering that the characteristics of extreme events have been suggested to change under ongoing anthropogenic climate change(5-8). Here we reveal the global coupling pattern of extreme-rainfall events by applying complex-network methodology to high-resolution satellite data and introducing a technique that corrects for multiple-comparison bias in functional networks. We find that the distance distribution of significant connections (P < 0.005) around the globe decays according to a power law up to distances of about 2,500 kilometres. For longer distances, the probability of significant connections is much higher than expected from the scaling of the power law. We attribute the shorter, power-law-distributed connections to regional weather systems. The longer, super-power-law-distributed connections form a global rainfall teleconnection pattern that is probably controlled by upper-level Rossby waves. We show that extreme-rainfall events in the monsoon systems of south-central Asia, east Asia and Africa are significantly synchronized. Moreover, we uncover concise links between south-central Asia and the European and North American extratropics, as well as the Southern Hemisphere extratropics. Analysis of the atmospheric conditions that lead to these teleconnections confirms Rossby waves as the physical mechanism underlying these global teleconnection patterns and emphasizes their crucial role in dynamical tropical-extratropical couplings. Our results provide insights into the function of Rossby waves in creating stable, global-scale dependencies of extreme-rainfall events, and into the potential predictability of associated natural hazards. Y1 - 2019 U6 - https://doi.org/10.1038/s41586-018-0872-x SN - 0028-0836 SN - 1476-4687 VL - 566 IS - 7744 SP - 373 EP - 377 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Kurths, Jürgen A1 - Agarwal, Ankit A1 - Shukla, Roopam A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Caesar, Levke A1 - Krishnan, Raghavan A1 - Merz, Bruno T1 - Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach JF - Nonlinear processes in geophysics N2 - A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting. Y1 - 2019 U6 - https://doi.org/10.5194/npg-26-251-2019 SN - 1023-5809 SN - 1607-7946 VL - 26 IS - 3 SP - 251 EP - 266 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Ciemer, Catrin A1 - Boers, Niklas A1 - Hirota, Marina A1 - Kurths, Jürgen A1 - Müller-Hansen, Finn A1 - Oliveira, Rafael S. A1 - Winkelmann, Ricarda T1 - Higher resilience to climatic disturbances in tropical vegetation exposed to more variable rainfall JF - Nature geoscience N2 - With ongoing global warming, the amount and frequency of precipitation in the tropics is projected to change substantially. While it has been shown that tropical forests and savannahs are sustained within the same intermediate mean annual precipitation range, the mechanisms that lead to the resilience of these ecosystems are still not fully understood. In particular, the long-term impact of rainfall variability on resilience is as yet unclear. Here we present observational evidence that both tropical forest and savannah exposed to a higher rainfall variability-in particular on interannual scales-during their long-term past are overall more resilient against climatic disturbances. Based on precipitation and tree cover data in the Brazilian Amazon basin, we constructed potential landscapes that enable us to systematically measure the resilience of the different ecosystems. Additionally, we infer that shifts from forest to savannah due to decreasing precipitation in the future are more likely to occur in regions with a precursory lower rainfall variability. Long-term rainfall variability thus needs to be taken into account in resilience analyses and projections of vegetation response to climate change. Y1 - 2019 U6 - https://doi.org/10.1038/s41561-019-0312-z SN - 1752-0894 SN - 1752-0908 VL - 12 IS - 3 SP - 174 EP - 179 PB - Nature Publ. Group CY - New York ER - TY - JOUR A1 - Agarwal, Ankit A1 - Maheswaran, Rathinasamy A1 - Marwan, Norbert A1 - Caesar, Levke A1 - Kurths, Jürgen T1 - Wavelet-based multiscale similarity measure for complex networks JF - The European physical journal : B, Condensed matter and complex systems N2 - In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales. KW - Statistical and Nonlinear Physics Y1 - 2018 U6 - https://doi.org/10.1140/epjb/e2018-90460-6 SN - 1434-6028 SN - 1434-6036 VL - 91 IS - 11 PB - Springer CY - New York ER - TY - JOUR A1 - Goswami, Bedartha A1 - Boers, Niklas A1 - Rheinwalt, Aljoscha A1 - Marwan, Norbert A1 - Heitzig, Jobst A1 - Breitenbach, Sebastian Franz Martin A1 - Kurths, Jürgen T1 - Abrupt transitions in time series with uncertainties JF - Nature Communications N2 - Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an ‘uncertainty-aware’ framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-017-02456-6 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Shukla, Roopam A1 - Agarwal, Ankit A1 - Sachdeva, Kamna A1 - Kurths, Jürgen A1 - Joshi, P. K. T1 - Climate change perception BT - an analysis of climate change and risk perceptions among farmer types of Indian Western Himalayas JF - Climatic change : an interdisciplinary, intern. journal devoted to the description, causes and implications of climatic change N2 - Climate change and variability have created widespread risks for farmers’ food and livelihood security in the Himalayas. However, the extent of impacts experienced and perceived by farmers varies, as there is substantial diversity in the demographic, social, and economic conditions. Therefore, it is essential to understand how farmers with different resource-endowment and household characteristics perceive climatic risks. This study aims to analyze how farmer types perceive climate change processes and its impacts to gain insight into locally differentiated concerns by farming communities. The present study is based in the Uttarakhand state of Indian Western Himalayas. We examine farmer perceptions of climate change and how perceived impacts differ across farmer types. Primary household interviews with farming households (n = 241) were done in Chakrata and Bhikiyasian tehsil in Uttarakhand, India. In addition, annual and seasonal patterns of historical data of temperature (1951–2013) and precipitation (1901–2013) were analyzed to estimate trends and validate farmers’ perception. Using statistical methods farmer typology was constructed, and five unique farmer types are identified. Majority of respondents across all farmer types noticed a decrease in summer and winter precipitation and an increase in summer temperature. Whereas the perceptions of impacts of climate change diverged across farmer types, as specific farmer types exclusively experienced few impacts. Impact of climatic risks on household food security and income was significantly perceived stronger by low-resource-endowed subsistence farmers, whereas the landless farmer type exclusively felt impacts on the communities social bond. This deeper understanding of the differentiated perception of impacts has strong implications for agricultural and development policymaking, highlighting the need for providing flexible adaptation options rather than specific solutions to avoid inequalities in fulfilling the needs of the heterogeneous farming communities. Y1 - 2018 U6 - https://doi.org/10.1007/s10584-018-2314-z SN - 0165-0009 SN - 1573-1480 VL - 152 IS - 1 SP - 103 EP - 119 PB - Springer CY - Dordrecht ER - TY - GEN A1 - Goswami, Bedartha A1 - Boers, Niklas A1 - Rheinwalt, Aljoscha A1 - Marwan, Norbert A1 - Heitzig, Jobst A1 - Breitenbach, Sebastian Franz Martin A1 - Kurths, Jürgen T1 - Abrupt transitions in time series with uncertainties T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Nino-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 576 KW - North-Atlantic climate KW - Indian monsoon KW - Holocene KW - teleconnections KW - variability KW - periods KW - records Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-423111 SN - 1866-8372 IS - 576 ER - TY - JOUR A1 - Ozturk, Ugur A1 - Marwan, Norbert A1 - Korup, Oliver A1 - Saito, H. A1 - Agarwa, Ankit A1 - Grossman, M. J. A1 - Zaiki, M. A1 - Kurths, Jürgen T1 - Complex networks for tracking extreme rainfall during typhoons JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons but mask out contributions of local convective storms. We propose a radial rank method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July. Y1 - 2018 U6 - https://doi.org/10.1063/1.5004480 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 7 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Agarwal, Ankit A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Merz, Bruno A1 - Kurths, Jürgen T1 - Quantifying the roles of single stations within homogeneous regions using complex network analysis JF - Journal of hydrology N2 - Regionalization and pooling stations to form homogeneous regions or communities are essential for reliable parameter transfer, prediction in ungauged basins, and estimation of missing information. Over the years, several clustering methods have been proposed for regional analysis. Most of these methods are able to quantify the study region in terms of homogeneity but fail to provide microscopic information about the interaction between communities, as well as about each station within the communities. We propose a complex network-based approach to extract this valuable information and demonstrate the potential of our approach using a rainfall network constructed from the Indian gridded daily precipitation data. The communities were identified using the network-theoretical community detection algorithm for maximizing the modularity. Further, the grid points (nodes) were classified into universal roles according to their pattern of within- and between-community connections. The method thus yields zoomed-in details of individual rainfall grids within each community. KW - Complex network KW - Event synchronization KW - Rainfall network KW - Z-P approach Y1 - 2018 U6 - https://doi.org/10.1016/j.jhydrol.2018.06.050 SN - 0022-1694 SN - 1879-2707 VL - 563 SP - 802 EP - 810 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Ramos, Antonio M. T. A1 - Builes-Jaramillo, Alejandro A1 - Poveda, German A1 - Goswami, Bedartha A1 - Macau, Elbert E. N. A1 - Kurths, Jürgen A1 - Marwan, Norbert T1 - Recurrence measure of conditional dependence and applications JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevE.95.052206 SN - 2470-0045 SN - 2470-0053 VL - 95 PB - American Physical Society CY - College Park ER - TY - GEN A1 - Hempel, Sabrina A1 - Koseska, Aneta A1 - Nikoloski, Zoran A1 - Kurths, Jürgen T1 - Unraveling gene regulatory networks from time-resolved gene expression data BT - a measures comparison study N2 - Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 371 KW - unferring cellular networks KW - mutual information KW - Escherichia-coli KW - cluster-analysis KW - series KW - algorithms KW - inference KW - models KW - recognition KW - variables Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400924 ER - TY - JOUR A1 - Agarwal, Ankit A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Merz, Bruno A1 - Kurths, Jürgen T1 - Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach JF - Nonlinear processes in geophysics N2 - The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales. Y1 - 2017 U6 - https://doi.org/10.5194/npg-24-599-2017 SN - 1023-5809 VL - 24 SP - 599 EP - 611 PB - Copernicus CY - Göttingen ER - TY - GEN A1 - Agarwal, Ankit A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Merz, Bruno A1 - Kurths, Jürgen T1 - Multi-scale event synchronization analysis for unravelling climate processes BT - a wavelet-based approach T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 661 KW - precipitation KW - phase KW - EEG KW - desynchronization KW - interdependences KW - coherence KW - networks KW - monsoon KW - models KW - time Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-418274 SN - 1866-8372 IS - 661 ER - TY - JOUR A1 - Agarwal, Ankit A1 - Maheswaran, Rathinasamy A1 - Kurths, Jürgen A1 - Khosa, R. T1 - Wavelet Spectrum and Self-Organizing Maps-Based Approach for Hydrologic Regionalization -a Case Study in the Western United States JF - Water Resources Management N2 - Hydrologic regionalization deals with the investigation of homogeneity in watersheds and provides a classification of watersheds for regional analysis. The classification thus obtained can be used as a basis for mapping data from gauged to ungauged sites and can improve extreme event prediction. This paper proposes a wavelet power spectrum (WPS) coupled with the self-organizing map method for clustering hydrologic catchments. The application of this technique is implemented for gauged catchments. As a test case study, monthly streamflow records observed at 117 selected catchments throughout the western United States from 1951 through 2002. Further, based on WPS of each station, catchments are classified into homogeneous clusters, which provides a representative WPS pattern for the streamflow stations in each cluster. KW - Wavelet power spectrum KW - Regionalization KW - Ungauged catchments KW - K-means technique KW - Self-organizing map Y1 - 2016 U6 - https://doi.org/10.1007/s11269-016-1428-1 SN - 0920-4741 SN - 1573-1650 VL - 30 SP - 4399 EP - 4413 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Rheinwalt, Aljoscha A1 - Boers, Niklas A1 - Marwan, Norbert A1 - Kurths, Jürgen A1 - Hoffmann, Peter A1 - Gerstengarbe, Friedrich-Wilhelm A1 - Werner, Peter T1 - Non-linear time series analysis of precipitation events using regional climate networks for Germany JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns. KW - Rainfall KW - Complex networks KW - Precipitation events KW - Anisotropy KW - Dominant link directions KW - Isochrones KW - Event synchronization Y1 - 2016 U6 - https://doi.org/10.1007/s00382-015-2632-z SN - 0930-7575 SN - 1432-0894 VL - 46 SP - 1065 EP - 1074 PB - Springer CY - New York ER - TY - JOUR A1 - Boers, Niklas A1 - Bookhagen, Bodo A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Spatiotemporal characteristics and synchronization of extreme rainfall in South America with focus on the Andes Mountain range JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to 50%). However, each consecutive episode of the infrequent events of type 4 still accounts for up to 20% of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately 20 degrees S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20 degrees S and the Puna Plateau originates from southeastern South America. KW - Extreme rainfall KW - Synchronization KW - Complex networks KW - South American monsoon system Y1 - 2016 U6 - https://doi.org/10.1007/s00382-015-2601-6 SN - 0930-7575 SN - 1432-0894 VL - 46 SP - 601 EP - 617 PB - Springer CY - New York ER - TY - JOUR A1 - Stolbova, Veronika A1 - Surovyatkina, Elena A1 - Bookhagen, Bodo A1 - Kurths, Jürgen T1 - Tipping elements of the Indian monsoon: Prediction of onset and withdrawal JF - Geophysical research letters N2 - Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation. Y1 - 2016 U6 - https://doi.org/10.1002/2016GL068392 SN - 0094-8276 SN - 1944-8007 VL - 43 SP - 3982 EP - 3990 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Traxl, Dominik A1 - Boers, Niklas A1 - Rheinwalt, Aljoscha A1 - Goswami, Bedartha A1 - Kurths, Jürgen T1 - The size distribution of spatiotemporal extreme rainfall clusters around the globe JF - Geophysical research letters N2 - The scaling behavior of rainfall has been extensively studied both in terms of event magnitudes and in terms of spatial extents of the events. Different heavy-tailed distributions have been proposed as candidates for both instances, but statistically rigorous treatments are rare. Here we combine the domains of event magnitudes and event area sizes by a spatiotemporal integration of 3-hourly rain rates corresponding to extreme events derived from the quasi-global high-resolution rainfall product Tropical Rainfall Measuring Mission 3B42. A maximum likelihood evaluation reveals that the distribution of spatiotemporally integrated extreme rainfall cluster sizes over the oceans is best described by a truncated power law, calling into question previous statements about scale-free distributions. The observed subpower law behavior of the distribution's tail is evaluated with a simple generative model, which indicates that the exponential truncation of an otherwise scale-free spatiotemporal cluster size distribution over the oceans could be explained by the existence of land masses on the globe. Y1 - 2016 U6 - https://doi.org/10.1002/2016GL070692 SN - 0094-8276 SN - 1944-8007 VL - 43 SP - 9939 EP - 9947 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Goswami, Bedartha A1 - Shekatkar, Snehal M. A1 - Rheinwalt, Aljoscha A1 - Ambika, G. A1 - Kurths, Jürgen T1 - A random interacting network model for complex networks JF - Scientific reports N2 - We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems. Y1 - 2015 U6 - https://doi.org/10.1038/srep18183 SN - 2045-2322 VL - 5 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Boers, Niklas A1 - Barbosa, Henrique M. J. A1 - Bookhagen, Bodo A1 - Marengo, Jose A. A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Propagation of Strong Rainfall Events from Southeastern South America to the Central Andes JF - Journal of climate N2 - Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes. KW - Cold air surges KW - Extreme events KW - Precipitation KW - Subtropical cyclones KW - Convective storms KW - Mesoscale systems Y1 - 2015 U6 - https://doi.org/10.1175/JCLI-D-15-0137.1 SN - 0894-8755 SN - 1520-0442 VL - 28 IS - 19 SP - 7641 EP - 7658 PB - American Meteorological Soc. CY - Boston ER - TY - JOUR A1 - Boers, Niklas A1 - Bookhagen, Bodo A1 - Marengo, Jose A1 - Marwan, Norbert A1 - von Storch, Jin-Song A1 - Kurths, Jürgen T1 - Extreme Rainfall of the South American Monsoon System: A Dataset Comparison Using Complex Networks JF - Journal of climate N2 - In this study, the authors compare six different rainfall datasets for South America with a focus on their representation of extreme rainfall during the monsoon season (December February): the gauge-calibrated TRMM 3B42 V7 satellite product; the near-real-time TRMM 3B42 V7 RT, the GPCP 1 degrees daily (1DD) V1.2 satellite gauge combination product, the Interim ECMWF Re-Analysis (ERA-Interim) product; output of a high-spatial-resolution run of the ECHAM6 global circulation model; and output of the regional climate model Eta. For the latter three, this study can be understood as a model evaluation. In addition to statistical values of local rainfall distributions, the authors focus on the spatial characteristics of extreme rainfall covariability. Since traditional approaches based on principal component analysis are not applicable in the context of extreme events, they apply and further develop methods based on complex network theory. This way, the authors uncover substantial differences in extreme rainfall patterns between the different datasets: (i) The three model-derived datasets yield very different results than the satellite gauge combinations regarding the main climatological propagation pathways of extreme events as well as the main convergence zones of the monsoon system. (ii) Large discrepancies are found for the development of mesoscale convective systems in southeastern South America. (iii) Both TRMM datasets and ECHAM6 indicate a linkage of extreme rainfall events between the central Amazon basin and the eastern slopes of the central Andes, but this pattern is not reproduced by the remaining datasets. The authors' study suggests that none of the three model-derived datasets adequately captures extreme rainfall patterns in South America. Y1 - 2015 U6 - https://doi.org/10.1175/JCLI-D-14-00340.1 SN - 0894-8755 SN - 1520-0442 VL - 28 IS - 3 SP - 1031 EP - 1056 PB - American Meteorological Soc. CY - Boston ER - TY - JOUR A1 - Eroglu, Deniz A1 - Marwan, Norbert A1 - Prasad, Sushma A1 - Kurths, Jürgen T1 - Finding recurrence networks' threshold adaptively for a specific time series JF - Nonlinear processes in geophysics N2 - Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches - recurrence plots and recurrence networks -, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record. Y1 - 2014 U6 - https://doi.org/10.5194/npg-21-1085-2014 SN - 1023-5809 VL - 21 IS - 6 SP - 1085 EP - 1092 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Goswami, Bedartha A1 - Heitzig, Jobst A1 - Rehfeld, Kira A1 - Marwan, Norbert A1 - Anoop, Ambili A1 - Prasad, Sushma A1 - Kurths, Jürgen T1 - Estimation of sedimentary proxy records together with associated uncertainty JF - Nonlinear processes in geophysics N2 - Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record. We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy-depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India. Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation. Y1 - 2014 U6 - https://doi.org/10.5194/npg-21-1093-2014 SN - 1023-5809 VL - 21 IS - 6 SP - 1093 EP - 1111 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Stolbova, Veronika A1 - Martin, P. A1 - Bookhagen, Bodo A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka JF - Nonlinear processes in geophysics N2 - This paper employs a complex network approach to determine the topology and evolution of the network of extreme precipitation that governs the organization of extreme rainfall before, during, and after the Indian Summer Monsoon (ISM) season. We construct networks of extreme rainfall events during the ISM (June-September), post-monsoon (October-December), and pre-monsoon (March-May) periods from satellite-derived (Tropical Rainfall Measurement Mission, TRMM) and rain-gauge interpolated (Asian Precipitation Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources, APHRODITE) data sets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns in North Pakistan (NP), the Eastern Ghats (EG), and the Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. These are important meteorological features that need further attention and that may be useful in ISM timing and strength prediction. Y1 - 2014 U6 - https://doi.org/10.5194/npg-21-901-2014 SN - 1023-5809 VL - 21 IS - 4 SP - 901 EP - 917 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Goswami, Bedartha A1 - Marwan, Norbert A1 - Feulner, Georg A1 - Kurths, Jürgen T1 - How do global temperature drivers influence each other? JF - European physical journal special topics N2 - We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations. Y1 - 2013 U6 - https://doi.org/10.1140/epjst/e2013-01889-8 SN - 1951-6355 VL - 222 IS - 3-4 SP - 861 EP - 873 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Marwan, Norbert A1 - Schinkel, Stefan A1 - Kurths, Jürgen T1 - Recurrence plots 25 years later -Gaining confidence in dynamical transitions JF - epl : a letters journal exploring the frontiers of physics N2 - Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots. Y1 - 2013 U6 - https://doi.org/10.1209/0295-5075/101/20007 SN - 0295-5075 VL - 101 IS - 2 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Bergner, Andre A1 - Frasca, M. A1 - Sciuto, G. A1 - Buscarino, A. A1 - Ngamga, Eulalie Joelle A1 - Fortuna, L. A1 - Kurths, Jürgen T1 - Remote synchronization in star networks JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.026208 SN - 1539-3755 VL - 85 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Marwan, Norbert A1 - Beller, Gise A1 - Felsenberg, Dieter A1 - Saparin, Peter A1 - Kurths, Jürgen T1 - quantifying changes in the spatial structure of trabecular bone JF - International journal of bifurcation and chaos : in applied sciences and engineering N2 - We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization. KW - 3D medical image analysis KW - pQCT KW - trabecular bone KW - patient immobilization Y1 - 2012 U6 - https://doi.org/10.1142/S0218127412500277 SN - 0218-1274 VL - 22 IS - 2 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Frasca, Mattia A1 - Bergner, Andre A1 - Kurths, Jürgen A1 - Fortuna, Luigi T1 - Bifurcations in a star-like network of Stuart-Landau oscillators JF - International journal of bifurcation and chaos : in applied sciences and engineering N2 - In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results. KW - Complex networks KW - synchronization KW - bifurcations Y1 - 2012 U6 - https://doi.org/10.1142/S0218127412501738 SN - 0218-1274 VL - 22 IS - 7 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Breitenbach, Sebastian Franz Martin A1 - Rehfeld, Kira A1 - Goswami, Bedartha A1 - Baldini, James U. L. A1 - Ridley, H. E. A1 - Kennett, D. J. A1 - Prufer, K. M. A1 - Aquino, Valorie V. A1 - Asmerom, Yemane A1 - Polyak, V. J. A1 - Cheng, Hai A1 - Kurths, Jürgen A1 - Marwan, Norbert T1 - Constructing Proxy Records from Age models (COPRA) JF - Climate of the past : an interactive open access journal of the European Geosciences Union N2 - Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question. We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage. Y1 - 2012 U6 - https://doi.org/10.5194/cp-8-1765-2012 SN - 1814-9324 VL - 8 IS - 5 SP - 1765 EP - 1779 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Malik, Nishant A1 - Zou, Y. A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Dynamical regimes and transitions in plio-pleistocene Asian monsoon JF - epl : a letters journal exploring the frontiers of physics N2 - We propose a novel approach based on the fluctuation of similarity to identify regimes of distinct dynamical complexity in short time series. A statistical test is developed to estimate the significance of the identified transitions. Our method is verified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real-world situation, we apply this method to identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of the solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the Walker circulation. Y1 - 2012 U6 - https://doi.org/10.1209/0295-5075/97/40009 SN - 0295-5075 VL - 97 IS - 4 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Srinivasan, K. A1 - Senthilkumar, D. V. A1 - Mohamed, I. Raja A1 - Murali, K. A1 - Lakshmanan, M. A1 - Kurths, Jürgen T1 - Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua's circuits without delay JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We construct a new RC phase shift network based Chua's circuit, which exhibits a period-doubling bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chua's oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS or CS is demonstrated without using a variable delay line both experimentally and numerically. Y1 - 2012 U6 - https://doi.org/10.1063/1.4711375 SN - 1054-1500 VL - 22 IS - 2 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Rusconi, Marco A1 - Valleriani, Angelo A1 - Dunlop, John William Chapman A1 - Kurths, Jürgen A1 - Weinkamer, Richard T1 - Quantitative approach to the stochastics of bone remodeling JF - epl : a letters journal exploring the frontiers of physics N2 - During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age. Y1 - 2012 U6 - https://doi.org/10.1209/0295-5075/97/28009 SN - 0295-5075 VL - 97 IS - 2 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Malik, Nishant A1 - Bookhagen, Bodo A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June-September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades. KW - Indian summer monsoon KW - Event synchronization KW - Complex networks KW - Rainfall patterns Y1 - 2012 U6 - https://doi.org/10.1007/s00382-011-1156-4 SN - 0930-7575 VL - 39 IS - 3-4 SP - 971 EP - 987 PB - Springer CY - New York ER - TY - JOUR A1 - Zakharova, Anna A1 - Kurths, Jürgen A1 - Vadivasova, Tatyana A1 - Koseska, Aneta T1 - Analysing dynamical behavior of cellular networks via stochastic bifurcations JF - PLoS one N2 - The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types. Y1 - 2011 U6 - https://doi.org/10.1371/journal.pone.0019696 SN - 1932-6203 VL - 6 IS - 5 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Srinivasan, K. A1 - Senthilkumar, Dharmapuri Vijayan A1 - Murali, K. A1 - Lakshmanan, Muthusamy A1 - Kurths, Jürgen T1 - Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay tau(1) and coupling delay tau(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay tau(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems. Y1 - 2011 U6 - https://doi.org/10.1063/1.3591791 SN - 1054-1500 VL - 21 IS - 2 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Hempel, Stefan A1 - Koseska, Aneta A1 - Kurths, Jürgen A1 - Nikoloski, Zoran T1 - Inner composition alignment for inferring directed networks from short time series JF - Physical review letters N2 - Identifying causal links (couplings) is a fundamental problem that facilitates the understanding of emerging structures in complex networks. We propose and analyze inner composition alignment-a novel, permutation-based asymmetric association measure to detect regulatory links from very short time series, currently applied to gene expression. The measure can be used to infer the direction of couplings, detect indirect (superfluous) links, and account for autoregulation. Applications to the gene regulatory network of E. coli are presented. Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevLett.107.054101 SN - 0031-9007 VL - 107 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Hempel, Sabrina A1 - Koseska, Aneta A1 - Nikoloski, Zoran A1 - Kurths, Jürgen T1 - Unraveling gene regulatory networks from time-resolved gene expression data - a measures comparison study JF - BMC bioinformatics N2 - Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices. Y1 - 2011 U6 - https://doi.org/10.1186/1471-2105-12-292 SN - 1471-2105 VL - 12 IS - 1 PB - BioMed Central CY - London ER - TY - JOUR A1 - Donges, Jonathan Friedemann A1 - Donner, Reik Volker A1 - Trauth, Martin H. A1 - Marwan, Norbert A1 - Schellnhuber, Hans Joachim A1 - Kurths, Jürgen T1 - Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution JF - Proceedings of the National Academy of Sciences of the United States of America N2 - Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa. KW - African climate KW - Plio-Pleistocene KW - climate-driven evolution KW - dynamical transitions KW - nonlinear time series analysis Y1 - 2011 U6 - https://doi.org/10.1073/pnas.1117052108 SN - 0027-8424 VL - 108 IS - 51 SP - 20422 EP - 20427 PB - National Acad. of Sciences CY - Washington ER - TY - JOUR A1 - Grimbs, Sergio A1 - Arnold, Anne A1 - Koseska, Aneta A1 - Kurths, Jürgen A1 - Selbig, Joachim A1 - Nikoloski, Zoran T1 - Spatiotemporal dynamics of the Calvin cycle multistationarity and symmetry breaking instabilities JF - Biosystems : journal of biological and information processing sciences N2 - The possibility of controlling the Calvin cycle has paramount implications for increasing the production of biomass. Multistationarity, as a dynamical feature of systems, is the first obvious candidate whose control could find biotechnological applications. Here we set out to resolve the debate on the multistationarity of the Calvin cycle. Unlike the existing simulation-based studies, our approach is based on a sound mathematical framework, chemical reaction network theory and algebraic geometry, which results in provable results for the investigated model of the Calvin cycle in which we embed a hierarchy of realistic kinetic laws. Our theoretical findings demonstrate that there is a possibility for multistationarity resulting from two sources, homogeneous and inhomogeneous instabilities, which partially settle the debate on multistability of the Calvin cycle. In addition, our tractable analytical treatment of the bifurcation parameters can be employed in the design of validation experiments. KW - Multistationarity KW - Calvin cycle KW - Algebraic geometry KW - Bifurcation parameters KW - Biomass Y1 - 2011 U6 - https://doi.org/10.1016/j.biosystems.2010.10.015 SN - 0303-2647 VL - 103 IS - 2 SP - 212 EP - 223 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Huang, Tingwen A1 - Chen, Guanrong A1 - Kurths, Jürgen T1 - Synchronization of chaotic of chaotic systems with time-varying coupöing delays JF - Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations N2 - In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation in equalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method. KW - Synchronization KW - Chaotic System KW - Time-varying Delay Y1 - 2011 U6 - https://doi.org/10.3934/dcdsb.2011.16.1071 SN - 1531-3492 VL - 16 IS - 4 SP - 1071 EP - 1082 PB - American Institute of Mathematical Sciences CY - Springfield ER - TY - JOUR A1 - Koseska, Aneta A1 - Volkov, Evgenii A1 - Kurths, Jürgen T1 - Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits JF - Physica scripta : an international journal for experimental and theoretical physics N2 - Synthetic biology is a relatively new research discipline that combines standard biology approaches with the constructive nature of engineering. Thus, recent efforts in the field of synthetic biology have given a perspective to consider cells as 'programmable matter'. Here, we address the possibility of using synthetic circuits to control protein dynamics. In particular, we show how intercellular communication and stochasticity can be used to manipulate the dynamical behavior of a population of coupled synthetic units and, in this manner, finely tune the expression of specific proteins of interest, e.g. in large bioreactors. Y1 - 2011 U6 - https://doi.org/10.1088/0031-8949/84/04/045007 SN - 0031-8949 VL - 84 IS - 4 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Donges, Jonathan Friedemann A1 - Donner, Reik Volker A1 - Rehfeld, Kira A1 - Marwan, Norbert A1 - Trauth, Martin H. A1 - Kurths, Jürgen T1 - Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis JF - Nonlinear processes in geophysics N2 - The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods. Y1 - 2011 U6 - https://doi.org/10.5194/npg-18-545-2011 SN - 1023-5809 VL - 18 IS - 5 SP - 545 EP - 562 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Wu, Ye A1 - Zhou, Changsong A1 - Chen, Maoyin A1 - Xiao, Jinghua A1 - Kurths, Jürgen T1 - Human comment dynamics in on-line social systems N2 - Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society. Y1 - 2010 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2010.08.049 SN - 0378-4371 ER - TY - JOUR A1 - Schmidt, G. A1 - Zamora-Lopez, Gorka A1 - Kurths, Jürgen T1 - Simulation of large scale cortical networks by individual neuron dynamics N2 - Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required. Y1 - 2010 U6 - https://doi.org/10.1142/S0218127410026149 SN - 0218-1274 ER - TY - JOUR A1 - Suresh, R. A1 - Senthilkumar, Dharmapuri Vijayan A1 - Lakshmanan, Muthusamy A1 - Kurths, Jürgen T1 - Global phase synchronization in an array of time-delay systems N2 - We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase. Y1 - 2010 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.82.016215 SN - 1539-3755 ER - TY - JOUR A1 - Vincent, Uchechukwu E. A1 - Kenfack, Anatole A1 - Senthilkumar, Dharmapuri Vijayan A1 - Mayer, Dieter A1 - Kurths, Jürgen T1 - Current reversals and synchronization in coupled ratchets N2 - Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k(th), a specific driving amplitude a(opt) is found for which the transport is optimum. Y1 - 2010 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.82.046208 SN - 1539-3755 ER - TY - JOUR A1 - Chen, Jin-Long A1 - Shiau, Yuo-Hsien A1 - Tseng, Yin-Jiun A1 - Chiu, Hung-Wen A1 - Hsiao, Tzu-Chien A1 - Wessel, Niels A1 - Kurths, Jürgen A1 - Chu, Woei-Chyn T1 - Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism : evidence from detrended fluctuation analysis of heart rate variability N2 - Despite many previous Studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent alpha 1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves' disease patients (32 females and 4 males; age 30 +/- 1 years, means +/- SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P < 0.001) in alpha 1 (hyperthyroid 1.28 +/- 0.04 versus control 0.91 +/- 0.02), long-term scaling exponent alpha 2 (1.05 +/- 0.02 versus 0.90 +/- 0.01), overall scaling exponent alpha (1.11 +/- 0.02 versus 0.89 +/- 0.01), low frequency power in normalized units (LF%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P < 0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients. Y1 - 2010 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2009.12.062 SN - 0378-4371 ER - TY - JOUR A1 - Itoh, Naoki A1 - Kurths, Jürgen T1 - Change-point detection of climate time series by nonparametric method N2 - In one of the data mining techniques, change-point detection is of importance in evaluating time series measured in real world. For decades this technique has been developed as a nonlinear dynamics. We apply the method for detecting the change points, Singular Spectrum Transformation (SST), to the climate time series. To know where the structures of climate data sets change can reveal a climate background. In this paper we discuss the structures of precipitation data in Kenya and Wrangel Island (Arctic land) by using the SST. Y1 - 2010 UR - http://www.doaj.org/doaj?func=openurl&issn=20780958&genre=journal SN - 2078-0958 ER - TY - JOUR A1 - Braun, Holger A1 - Ditlevsen, Peter D. A1 - Kurths, Jürgen A1 - Mudelsee, Manfred T1 - Limitations of red noise in analysing Dansgaard-Oeschger events N2 - During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions. Y1 - 2010 UR - http://www.clim-past.net/volumes_and_issues.html U6 - https://doi.org/10.5194/cp-6-85-2010 SN - 1814-9324 ER - TY - JOUR A1 - Wu, Ye Wu A1 - Zhou, Changsong A1 - Xiao, Jinghua A1 - Kurths, Jürgen A1 - Schellnhuber, Hans Joachim T1 - Evidence for a bimodal distribution in human communication N2 - Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc. Y1 - 2010 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1073/pnas.1013140107 SN - 0027-8424 ER - TY - JOUR A1 - Zakharova, Anna A1 - Vadivasova, Tatjana A1 - Anishchenko, Vadim S. A1 - Koseska, Aneta A1 - Kurths, Jürgen T1 - Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator N2 - We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs. Y1 - 2010 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.81.011106 SN - 1539-3755 ER - TY - JOUR A1 - Helland, Vanessa Carolina Figuera A1 - Gapelyuk, Andrej A1 - Suhrbier, Alexander A1 - Riedl, Maik A1 - Penzel, Thomas A1 - Kurths, Jürgen A1 - Wessel, Niels T1 - Investigation of an automatic sleep stage classification by means of multiscorer hypnogram N2 - Objectives: Scoring sleep visually based on polysomnography is an important but time-consuming element of sleep medicine. Where-as computer software assists human experts in the assignment of sleep stages to polysomnogram epochs, their performance is usually insufficient. This study evaluates the possibility to fully automatize sleep staging considering the reliability of the sleep stages available from human expert sleep scorers. Methods: We obtain features from EEG, ECG and respiratory signals of polysomnograms from ten healthy subjects. Using the sleep stages provided by three human experts, we evaluate the performance of linear discriminant analysis on the entire polysomnogram and:only on epochs where the three experts agree in their-sleep stage scoring. Results: We show that in polysomnogram intervals, to which all three scorers assign the same sleep stage, our algorithm achieves 90% accuracy. This high rate of agreement with the human experts is accomplished with only a small set of three frequency features from the EEG. We increase-the performance to 93% by including ECG and respiration features. In contrast, on intervals of ambiguous sleep stage, the sleep stage classification obtained from our algorithm, agrees with the human consensus scorer in approximately 61%. Conclusions: These findings suggest that machine classification is highly consistent with human sleep staging and that error in the algorithm's assignments is rather a problem of lack of well-defined criteria for human experts to judge certain polysomnogram epochs than an insufficiency of computational procedures Y1 - 2010 UR - http://www.schattauer.de/index.php?id=103&L=1 U6 - https://doi.org/10.3414/Me09-02-0052 SN - 0026-1270 ER - TY - JOUR A1 - Senthilkumar, Dharmapuri Vijayan A1 - Kurths, Jürgen T1 - Characteristics and synchronization of time-delay systems driven by a common noise N2 - We investigate the characteristics of time-delay systems in the presence of Gaussian noise. We show that the delay time embedded in the time series of time-delay system with constant delay cannot be estimated in the presence noise for appropriate values of noise intensity thereby forbidding any possibility of phase space reconstruction. We also demonstrate the existence of complete synchronization between two independent identical time-delay systems driven by a common noise without explicitly establishing any external coupling between them. Y1 - 2010 UR - http://www.springerlink.com/content/1951-6355 U6 - https://doi.org/10.1140/epjst/e2010-01273-4 SN - 1951-6355 ER - TY - JOUR A1 - Orgis, Thomas A1 - Brand, Sascha A1 - Schwarz, Udo A1 - Handorf, Dörthe A1 - Dethloff, Klaus A1 - Kurths, Jürgen T1 - Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model N2 - A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex. Y1 - 2009 UR - http://www.springerlink.com/content/1951-6355 U6 - https://doi.org/10.1140/epjst/e2009-01105-8 SN - 1951-6355 ER - TY - GEN A1 - Koseska, Aneta A1 - Zaikin, Alexey A1 - Kurths, Jürgen A1 - García-Ojalvo, Jordi T1 - Timing cellular decision making under noise via cell-cell communication N2 - Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 148 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45260 ER - TY - JOUR A1 - Komalapriya, Chandrasekaran A1 - Romano Blasco, Maria Carmen A1 - Thiel, Marco A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Simonotto, Jennifer A1 - Furman, Michael A1 - Ditto, William L. A1 - Carney, Paul R. T1 - Analysis of high-resulution microelectrode EEG recordings in an animal model of spontaneous limbic seizures Y1 - 2009 UR - http://www.worldscinet.com/ijbc/ijbc.shtml U6 - https://doi.org/10.1142/S0218127409023226 SN - 0218-1274 ER - TY - JOUR A1 - Marwan, Norbert A1 - Kurths, Jürgen A1 - Thomsen, Jesper Skovhus A1 - Felsenberg, Dieter A1 - Saparin, Peter T1 - Three-dimensional quantification of structures in trabecular bone using measures of complexity N2 - The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography (mu CT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mu CT data sets. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.79.021903 SN - 1539-3755 ER - TY - JOUR A1 - Li, Ping A1 - Chen, Maoyin A1 - Wu, Ye A1 - Kurths, Jürgen T1 - Matrix-measure criterion for synchronization in coupled-map networks N2 - We present conditions for the local and global synchronizations in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.79.067102 SN - 1539-3755 ER - TY - JOUR A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. : [Physica D 237 (2008) 619-629] N2 - In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/01672789 U6 - https://doi.org/10.1016/j.physd.2009.04.018 SN - 0167-2789 ER - TY - JOUR A1 - Florence, Gerson A1 - Dahlem, Markus A. A1 - Almeida, Antônio-Carlos G. A1 - Bassani, José W. M. A1 - Kurths, Jürgen T1 - The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study N2 - Experimental evidences point Out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular tons) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K+](o) and a decrease of extracellular calcium concentration [Ca2+](o) which raises the neuronal excitability. However, whether the high [K+](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K+](o) and zero [Ca2+](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na+-K+ pump, ion diffusion and glial buffering. Within these Conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na+- K+ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K+ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K+](o), transiting to an elevated state of neuronal excitability. Effects of high [K+](o), are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K+](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K+](o) by outward K+ flow depresses K+ Currents in a positive feedback way. At the last stage, due to the depression of K+ currents, the Na+-K+ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K+](o) dynamics may play a fundamental role in these abnormal oscillatory patterns. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/00225193 U6 - https://doi.org/10.1016/j.jtbi.2009.01.032 SN - 0022-5193 ER - TY - JOUR A1 - Donges, Jonathan Friedemann A1 - Zou, Yong A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Complex networks in climate dynamics : comparing linear and nonlinear network construction methods N2 - Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system. Y1 - 2009 UR - http://www.springerlink.com/content/1951-6355 U6 - https://doi.org/10.1140/epjst/e2009-01098-2 SN - 1951-6355 ER - TY - JOUR A1 - Wessel, Niels A1 - Riedl, Maik A1 - Kurths, Jürgen T1 - Is the normal heart rate "chaotic" due to respiration? N2 - The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: " Is the normal heart rate 'chaotic' due to respiration?" Y1 - 2009 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.3133128 SN - 1054-1500 ER - TY - JOUR A1 - Wu, Ye A1 - Li, Ping A1 - Chen, Maoyin A1 - Xiao, Jinghua A1 - Kurths, Jürgen T1 - Response of scale-free networks with community structure to external stimuli N2 - The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2009.03.037 SN - 0378-4371 ER - TY - JOUR A1 - Sun, Xiaojuan A1 - Lu, Qishao A1 - Kurths, Jürgen A1 - Wang, Qingyun T1 - Spatiotemporal coherence resonance in a map lattice N2 - We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively. Y1 - 2009 UR - http://www.worldscinet.com/ijbc/ijbc.shtml U6 - https://doi.org/10.1142/S021812740902310X SN - 0218-1274 ER - TY - JOUR A1 - Fujiwara, Naoya A1 - Kurths, Jürgen T1 - Spectral universality of phase synchronization in non-identical oscillator networks N2 - We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise. Y1 - 2009 UR - http://www.springerlink.com/content/101159 U6 - https://doi.org/10.1140/epjb/e2009-00078-6 SN - 1434-6028 ER - TY - JOUR A1 - Koseska, Aneta A1 - Volkov, Evgenij A1 - Kurths, Jürgen T1 - Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators N2 - We study dynamical regimes of globally coupled genetic relaxation oscillators in the presence of small detuning. Using bifurcation analysis, we find that under strong coupling via the slow variable, the detuning can eliminate standard oscillatory solutions in a large region of the parameter space, providing the dominance of oscillation death. This result is substantially different from previous results on oscillation quenching, where for homogeneous populations, the coexistence of oscillation death and limit cycle oscillations is always present. We propose further that this effect of detuning-dependent dominance could be a powerful regulator of genetic network's dynamics. Y1 - 2009 UR - http://iopscience.iop.org/0295-5075/ U6 - https://doi.org/10.1209/0295-5075/85/28002 SN - 0295-5075 ER - TY - JOUR A1 - Retzlaff, Beatrice A1 - Bauernschmitt, Robert A1 - Malberg, Hagen A1 - Brockmann, Gernot A1 - Uhl, Christian A1 - Lange, Ruediger A1 - Kurths, Jürgen A1 - Bretthauer, Georg A1 - Wessel, Niels T1 - Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma N2 - The analysis of baroreflex sensitivity (BRS) and heart rate variability (HRV) leads to additional insights into patients' prognosis after cardiovascular events. The following study was performed to assess the differences in the post-operative recovery of autonomic regulation after mitral valve (MV) and aortic valve (AV) surgery with a heart lung machine. Among the 43 consecutive male patients enrolled in a prospective study, 26 underwent isolated AV surgery and 17 isolated MV surgery. Blood pressure as well as ECG signals were recorded the day before, 24 hours after and one week after surgery. BRS was calculated according to the dual sequence method, and HRV was calculated using standard linear as well as nonlinear parameters. There were no major differences between the two groups in the pre-operative values. At 24 hours a comparable depression of HRV and BRS in both groups was observed, while at 7 days there was partial recovery in AV patients, which was absent in MV patients: p(AV versus MV) < 0.001. While the response of the autonomic system to surgery is similar in AV and MV patients, there is obviously a decreased ability to recover in MV patients, probably attributed to traumatic lesions of the autonomic nervous system by opening the atria. Ongoing research is required for further clarification of the pathophysiology of this phenomenon and to establish strategies to restore autonomic function. Y1 - 2009 UR - http://rsta.royalsocietypublishing.org/ U6 - https://doi.org/10.1098/rsta.2008.0272 SN - 1364-503X ER - TY - JOUR A1 - Pavlov, Alexey N. A1 - Anisimov, A. A. A1 - Semyachkina-Glushkovskaya, Oxana V. A1 - Matasova, E. G. A1 - Kurths, Jürgen T1 - Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform N2 - We study gender-related particularities in cardiovascular responses to stress and nitric oxide (NO) deficiency in rats using HR, mean arterial pressure (MAP) and a proposed wavelet-based approach. Blood pressure dynamics is analyzed: (1) under control conditions, (2) during immobilization stress and recovery and (3) during nitric oxide blockade by N-G-nitro-L-arginine-methyl ester (L-NAME). We show that cardiovascular sensitivity to stress and NO deficiency depends upon gender. Actually, in females the chronotropic effect of stress is more pronounced, while the pressor effect is weakened compared with males. We conclude that females demonstrate more favorable patterns of cardiovascular responses to stress and more effective NO control of cardiovascular activity than males. Y1 - 2009 UR - http://iopscience.iop.org/0967-3334/ U6 - https://doi.org/10.1088/0967-3334/30/7/013 SN - 0967-3334 ER - TY - JOUR A1 - Pereira, Tiago A1 - Baptista, Murilo da Silva A1 - Reyes, Marcelo B. A1 - Caldas, Ibere Luiz A1 - Sartorelli, José Carlos A1 - Kurths, Jürgen T1 - A scenario for torus T-2 destruction via a global bifurcation N2 - We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T-2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type- if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/09600779 U6 - https://doi.org/10.1016/j.chaos.2007.06.115 SN - 0960-0779 ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Kurths, Jürgen A1 - Mergenthaler, Konstantin A1 - Engbert, Ralf T1 - Hypothesis test for synchronization : twin surrogates revisited N2 - The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes. Y1 - 2009 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.3072784 SN - 1054-1500 ER - TY - JOUR A1 - Rusconi, Marco A1 - Valleriani, Angelo A1 - Dunlop, John William Chapman A1 - Kurths, Jürgen A1 - Weinkamer, Richard T1 - Insights into the control of trabecular bone remodelling obtained by a Markov model Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/87563282 U6 - https://doi.org/10.1016/j.bone.2009.03.467 SN - 8756-3282 ER - TY - JOUR A1 - Porta, Alberto A1 - Di Rienzo, Marco A1 - Wessel, Niels A1 - Kurths, Jürgen T1 - Addressing the complexity of cardiovascular regulation Y1 - 2009 UR - http://rsta.royalsocietypublishing.org/ U6 - https://doi.org/10.1098/rsta.2008.0292 SN - 1364-503X ER - TY - JOUR A1 - Schinkel, Stefan A1 - Marwan, Norbert A1 - Dimigen, Olaf A1 - Kurths, Jürgen T1 - Confidence bounds of recurrence-based complexity measures N2 - In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/03759601 U6 - https://doi.org/10.1016/j.physleta.2009.04.045 SN - 0375-9601 ER - TY - JOUR A1 - Chen, Maoyin A1 - Shang, Yun A1 - Zhou, Changsong A1 - Wu, Ye A1 - Kurths, Jürgen T1 - Enhanced synchronizability in scale-free networks N2 - We introduce a modified dynamical optimization coupling scheme to enhance the synchronizability in the scale- free networks as well as to keep uniform and converging intensities during the transition to synchronization. Further, the size of networks that can be synchronizable exceeds by several orders of magnitude the size of unweighted networks. Y1 - 2009 UR - http://chaos.aip.org/ U6 - https://doi.org/10.1063/1.3062864 SN - 1054-1500 ER - TY - JOUR A1 - Zolotova, Nadezhda V. A1 - Ponyavin, Dmitri I. A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Long-term asymmetry in the wings of the butterfly diagram N2 - Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator. Y1 - 2009 UR - http://www.aanda.org/ U6 - https://doi.org/10.1051/0004-6361/200811430 SN - 0004-6361 ER - TY - JOUR A1 - Schinkel, Stefan A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Brain signal analysis based on recurrences N2 - The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/09284257 U6 - https://doi.org/10.1016/j.jphysparis.2009.05.007 SN - 0928-4257 ER - TY - JOUR A1 - Zamora-Lopez, Gorka A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Graph analysis of cortical networks reveals complex anatomical communication substrate N2 - Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (i) a large density of connections, (ii) segregation of cortical areas into clusters, and (iii) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other. Y1 - 2009 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.3089559 SN - 1054-1500 ER - TY - JOUR A1 - Riedl, Maik A1 - van Leeuwen, Peter Jan A1 - Suhrbier, Alexander A1 - Malberg, Hagen A1 - Groenemeyer, Dietrich A1 - Kurths, Jürgen A1 - Wessel, Niels T1 - Testing foetal-maternal heart rate synchronization via model-based analyses N2 - The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization. Y1 - 2009 UR - http://rsta.royalsocietypublishing.org/ U6 - https://doi.org/10.1098/rsta.2008.0277 SN - 1364-503X ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin A1 - Kliegl, Reinhold T1 - Generating surrogates from recurrences N2 - In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres. Y1 - 2008 UR - http://rsta.royalsocietypublishing.org/ SN - 1364-503X ER - TY - JOUR A1 - Moshel, Shay A1 - Zivotofsky, Ari Z. A1 - Liang, Jin-Rong A1 - Engbert, Ralf A1 - Kurths, Jürgen A1 - Kliegl, Reinhold A1 - Havlin, Shlomo T1 - Persistence and phase synchronization properties of fixational eye movement N2 - When we fixate our gaze on a stable object, our eyes move continuously with extremely small involuntary and autonomic movements, that even we are unaware of during their occurrence. One of the roles of these fixational eye movements is to prevent the adaptation of the visual system to continuous illumination and inhibit fading of the image. These random, small movements are restricted at long time scales so as to keep the target at the centre of the field of view. In addition, the synchronisation properties between both eyes are related to binocular coordination in order to provide stereopsis. We investigated the roles of different time scale behaviours, especially how they are expressed in the different spatial directions (vertical versus horizontal). We also tested the synchronisation between both eyes. Results show different scaling behaviour between horizontal and vertical movements. When the small ballistic movements, i.e., microsaccades, are removed, the scaling behaviour in both axes becomes similar. Our findings suggest that microsaccades enhance the persistence at short time scales mostly in the horizontal component and much less in the vertical component. We also applied the phase synchronisation decay method to study the synchronisation between six combinations of binocular fixational eye movement components. We found that the vertical-vertical components of right and left eyes are significantly more synchronised than the horizontal-horizontal components. These differences may be due to the need for continuously moving the eyes in the horizontal plane in order to match the stereoscopic image for different viewing distances. Y1 - 2008 UR - 1960 = DOI: 10.1140/epjst/e2008-00762-3 SN - 1951-6355 ER - TY - JOUR A1 - Baptista, Murilo da Silva A1 - Bohn, Christiane A1 - Kliegl, Reinhold A1 - Engbert, Ralf A1 - Kurths, Jürgen T1 - Reconstruction of eye movements during blinks Y1 - 2008 UR - http://chaos.aip.org/ U6 - https://doi.org/10.1063/1.2890843 SN - 1054-1500 ER - TY - JOUR A1 - Palus, Milan A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Seehafer, Norbert A1 - Novotna, Dagmar A1 - Charvatova, Ivanka T1 - The solar activity cycle is weakly synchronized with the solar inertial motion N2 - We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM. Y1 - 2007 UR - http://www.sciencedirect.com/ science?_ob=GatewayURL&_method=citationSearch&_urlVersion=4&_origin=SDVIALERTHTML&_version=1&_uoikey=B6TVM-4MYVG5S- 1&md5=92d1fc7094be5195504f17e1afb4f0d1 U6 - https://doi.org/10.1016/j.physleta.2007.01.039 ER - TY - BOOK A1 - Osipov, Grigory V. A1 - Kurths, Jürgen A1 - Zhou, Changsong T1 - Synchronisation in Oscillatory Networks Y1 - 2007 SN - 978-3-540-71268-8 PB - Springer-Verlag CY - Berlin ER - TY - JOUR A1 - Zaikin, Alexey A1 - Kurths, Jürgen T1 - Optimal length transportation hypothesis to model proteasome product size distribution JF - Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences N2 - This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport. KW - proteasome KW - protein translocation KW - stochastic process KW - ratchets Y1 - 2006 U6 - https://doi.org/10.1007/s10867-006-9014-z SN - 0092-0606 VL - 32 IS - 3-4 SP - 231 EP - 243 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Winterhalder, Matthias A1 - Schelter, B A1 - Kurths, Jürgen A1 - Schulze-Borthage, A A1 - Timmer, Jens T1 - Sensitivity and specificity of coherence and phase synchronization analysis N2 - In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved Y1 - 2006 UR - http://www.sciencedirect.com/science/article/pii/S0375960106004002 ( 11.07.2011] U6 - https://doi.org/10.1016/j.physleta.2006.03.018 ER - TY - JOUR A1 - Dana, Syamal Kumar A1 - Blasius, Bernd A1 - Kurths, Jürgen T1 - Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators N2 - We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models Y1 - 2006 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.2197168 SN - 1054-1500 ER - TY - JOUR A1 - Vasconcelos, D. B. A1 - Lopes, S. R. A1 - Viana, R. L. A1 - Kurths, Jürgen T1 - Spatial recurrence plots N2 - We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes Y1 - 2006 UR - http://pre.aps.org/pdf/PRE/v73/i5/e056207 U6 - https://doi.org/10.1103/Physreve.73.056207 ER - TY - JOUR A1 - Baptista, Murilo da Silva A1 - Pereira, Tiago A1 - Kurths, Jürgen T1 - Upper bounds in phase synchronous weak coherent chaotic attractors N2 - An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/01672789 U6 - https://doi.org/10.1016/j.physd.2006.02.007 SN - 0167-2789 ER - TY - JOUR A1 - Raab, Corinna A1 - Wessel, Niels A1 - Schirdewan, Alexander A1 - Kurths, Jürgen T1 - Large-scale dimension densities for heart rate variability analysis N2 - In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.041907 SN - 1539-3755 ER - TY - JOUR A1 - Anishchenko, Vadim S. A1 - Nikolaev, S A1 - Kurths, Jürgen T1 - Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions N2 - We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.056202 SN - 1539-3755 ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Hwang, Dong-Uk A1 - Chavez, Mario A1 - Amann, Andreas A1 - Kurths, Jürgen A1 - Pecora, Louis M. T1 - Synchronization in dynamical networks : evolution along commutative graphs N2 - Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.74.016102 SN - 1539-3755 ER -