@article{SrinivasanSenthilkumarMohamedetal.2012, author = {Srinivasan, K. and Senthilkumar, D. V. and Mohamed, I. Raja and Murali, K. and Lakshmanan, M. and Kurths, J{\"u}rgen}, title = {Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua's circuits without delay}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {22}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {2}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4711375}, pages = {8}, year = {2012}, abstract = {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.}, language = {en} } @article{KurthsSchwarz1993, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Application of techniques of nonlinear dynamics to SS Cyg}, isbn = {0-7503-0282-8}, year = {1993}, abstract = {We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor.}, language = {en} } @article{ZhouKurthsHu2001, author = {Zhou, Changsong and Kurths, J{\"u}rgen and Hu, B.}, title = {Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise}, year = {2001}, language = {en} } @article{OsipovRosenblumPikovskijetal.1997, author = {Osipov, Grigory V. and Rosenblum, Michael and Pikovskij, Arkadij and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization}, year = {1997}, abstract = {The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.}, language = {en} } @article{AnishchenkoVadivasovaKurthsetal.2004, author = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kurths, J{\"u}rgen and Okrokvertskhov, G. A. and Strelkova, G. I.}, title = {Autocorrelation function and spectral linewidth of spiral chaos in a physical experiment}, issn = {1063-651X}, year = {2004}, abstract = {We present results of physical experiments where we measure the autocorrelation function (ACF) and the spectral linewidth of the basic frequency of a spiral chaotic attractor in a generator with inertial nonlinearity both without and in the presence of external noise. It is shown that the ACF of spiral attractors decays according to an exponential law with a decrement which is defined by the phase diffusion coefficient. It is also established that the evolution of the instantaneous phase can be approximated by a Wiener random process}, language = {en} } @article{BelykhOsipovKucklaenderetal.2005, author = {Belykh, Vladimir N. and Osipov, Grigory V. and Kuckl{\"a}nder, Nina and Blasius, Bernd and Kurths, J{\"u}rgen}, title = {Automatic control of phase synchronization in coupled complex oscillators}, year = {2005}, abstract = {We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.}, language = {en} } @article{FrascaBergnerKurthsetal.2012, author = {Frasca, Mattia and Bergner, Andre and Kurths, J{\"u}rgen and Fortuna, Luigi}, title = {Bifurcations in a star-like network of Stuart-Landau oscillators}, series = {International journal of bifurcation and chaos : in applied sciences and engineering}, volume = {22}, journal = {International journal of bifurcation and chaos : in applied sciences and engineering}, number = {7}, publisher = {World Scientific}, address = {Singapore}, issn = {0218-1274}, doi = {10.1142/S0218127412501738}, pages = {13}, year = {2012}, abstract = {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.}, language = {en} } @article{GowinSaparinKurthsetal.2001, author = {Gowin, W. and Saparin, Peter and Kurths, J{\"u}rgen and Felsenberg, D.}, title = {Bone Architecture assessment with Measures of Complexity}, year = {2001}, language = {en} } @article{GowinSaparinKurths2001, author = {Gowin, W. and Saparin, Peter and Kurths, J{\"u}rgen}, title = {Bone architecture quantification: Measures of complexity compared to failure lead results}, year = {2001}, language = {en} } @article{SchinkelMarwanKurths2009, author = {Schinkel, Stefan and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Brain signal analysis based on recurrences}, issn = {0928-4257}, doi = {10.1016/j.jphysparis.2009.05.007}, year = {2009}, abstract = {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.}, language = {en} } @article{VianaGrebogiPintoetal.2005, author = {Viana, R. L. and Grebogi, Celso and Pinto, S. E. D. and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen}, title = {Bubbling bifurcation : loss of synchronization and shadowing breakdown in complex systems}, year = {2005}, abstract = {Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved}, language = {en} } @article{ItohKurths2010, author = {Itoh, Naoki and Kurths, J{\"u}rgen}, title = {Change-point detection of climate time series by nonparametric method}, issn = {2078-0958}, year = {2010}, abstract = {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.}, language = {en} } @article{KurthsSchwarz1994, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Chaos theory and radio emission}, year = {1994}, abstract = {The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct.}, language = {en} } @article{BaptistaKurths2005, author = {Baptista, Murilo da Silva and Kurths, J{\"u}rgen}, title = {Chaotic channel}, issn = {1539-3755}, year = {2005}, abstract = {This work combines the theory of chaotic synchronization with the theory of information in order to introduce the chaotic channel, an active medium formed by connected chaotic systems. This subset of a large chaotic net represents the path along which information flows. We show that the possible amount of information exchange between the transmitter, where information enters the net, and the receiver, the destination of the information, is proportional to the level of synchronization between these two special subsystems}, language = {en} } @article{SenthilkumarKurths2010, author = {Senthilkumar, Dharmapuri Vijayan and Kurths, J{\"u}rgen}, title = {Characteristics and synchronization of time-delay systems driven by a common noise}, issn = {1951-6355}, doi = {10.1140/epjst/e2010-01273-4}, year = {2010}, abstract = {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.}, language = {en} } @unpublished{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556}, year = {1997}, abstract = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.}, language = {en} } @book{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, series = {Preprint NLD}, volume = {36}, journal = {Preprint NLD}, publisher = {Univ. Potsdam}, address = {Potsdam}, issn = {1432-2935}, pages = {20 S. : graph. Darst.}, year = {1997}, language = {en} } @article{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Charakterizing the dynamics of stochastic bistable systems by measures of complexity}, year = {1997}, language = {en} } @article{ShuklaAgarwalSachdevaetal.2018, author = {Shukla, Roopam and Agarwal, Ankit and Sachdeva, Kamna and Kurths, J{\"u}rgen and Joshi, P. K.}, title = {Climate change perception}, series = {Climatic change : an interdisciplinary, intern. journal devoted to the description, causes and implications of climatic change}, volume = {152}, journal = {Climatic change : an interdisciplinary, intern. journal devoted to the description, causes and implications of climatic change}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {0165-0009}, doi = {10.1007/s10584-018-2314-z}, pages = {103 -- 119}, year = {2018}, abstract = {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.}, language = {en} } @article{MarwanTrauthSchwarzetal.1999, author = {Marwan, Norbert and Trauth, Martin H. and Schwarz, Udo and Kurths, J{\"u}rgen and Strecker, Manfred}, title = {Climate dynamics of varved pleistocene lake sediments in nw Argentina}, issn = {1029-7006}, year = {1999}, language = {en} } @article{SpahnKatzorkePetzschmannetal.1997, author = {Spahn, Frank and Katzorke, Ines and Petzschmann, Olaf and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {Cluster instabiliy of granular assemblies}, year = {1997}, language = {en} } @article{SpahnSchwarzKurths1997, author = {Spahn, Frank and Schwarz, Udo and Kurths, J{\"u}rgen}, title = {Clustering of granular assemblies with temperature dependent restitution under Keplerian differential rotation}, year = {1997}, language = {en} } @article{PikovskijKurths1997, author = {Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Coherence Resonance in a Noise-Driven Excitable System}, year = {1997}, abstract = {We study the dynamics of the excitable Fitz Hugh-Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon.}, language = {en} } @article{PikovskijKurths1997, author = {Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Coherence resonance in a noise-driven excitable system}, year = {1997}, language = {en} } @article{KopitzkiWarnkeSaparinetal.2002, author = {Kopitzki, K. and Warnke, P. C. and Saparin, Peter and Kurths, J{\"u}rgen and Timmer, Jens}, title = {Comment on "Kullback-Leibler and renormalized entropies: Applications to electroencephalograms of epilepsy patients"}, year = {2002}, language = {en} } @article{RosenblumKurthsPikovskij2001, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij}, title = {Comment on "Phase synchronization in discrete chaotic systems"}, year = {2001}, abstract = {Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.}, language = {en} } @article{MarwanKurths2009, author = {Marwan, Norbert and Kurths, J{\"u}rgen}, title = {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]}, issn = {0167-2789}, doi = {10.1016/j.physd.2009.04.018}, year = {2009}, abstract = {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.}, language = {en} } @article{MarwanTrauthVuilleetal.2003, author = {Marwan, Norbert and Trauth, Martin H. and Vuille, Mathias and Kurths, J{\"u}rgen}, title = {Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods}, year = {2003}, abstract = {Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26°S, 66°W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Ni{\~n}o/ Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.}, language = {en} } @article{HassanKurths2001, author = {Hassan, M. K. and Kurths, J{\"u}rgen}, title = {Competitive random sequential adsorption of point and fixed-sized particles: analytical results}, year = {2001}, language = {en} } @article{OzturkMarwanKorupetal.2018, author = {Ozturk, Ugur and Marwan, Norbert and Korup, Oliver and Saito, H. and Agarwa, Ankit and Grossman, M. J. and Zaiki, M. and Kurths, J{\"u}rgen}, title = {Complex networks for tracking extreme rainfall during typhoons}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {7}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5004480}, pages = {8}, year = {2018}, abstract = {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.}, language = {en} } @article{DongesZouMarwanetal.2009, author = {Donges, Jonathan and Zou, Yong and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Complex networks in climate dynamics : comparing linear and nonlinear network construction methods}, issn = {1951-6355}, doi = {10.1140/epjst/e2009-01098-2}, year = {2009}, abstract = {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.}, language = {en} } @article{BoersGoswamiRheinwaltetal.2019, author = {Boers, Niklas and Goswami, Bedartha and Rheinwalt, Aljoscha and Bookhagen, Bodo and Hoskins, Brian and Kurths, J{\"u}rgen}, title = {Complex networks reveal global pattern of extreme-rainfall teleconnections}, series = {Nature : the international weekly journal of science}, volume = {566}, journal = {Nature : the international weekly journal of science}, number = {7744}, publisher = {Nature Publ. Group}, address = {London}, issn = {0028-0836}, doi = {10.1038/s41586-018-0872-x}, pages = {373 -- 377}, year = {2019}, abstract = {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.}, language = {en} } @article{RomanoThielSchwarzetal.2001, author = {Romano, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Lange, Holger and Hauhs, M.}, title = {Conceptual model of runoff from a forested catchment}, year = {2001}, abstract = {We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data.}, language = {en} } @article{ChenShiauTsengetal.2010, author = {Chen, Jin-Long and Shiau, Yuo-Hsien and Tseng, Yin-Jiun and Chiu, Hung-Wen and Hsiao, Tzu-Chien and Wessel, Niels and Kurths, J{\"u}rgen and Chu, Woei-Chyn}, title = {Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism : evidence from detrended fluctuation analysis of heart rate variability}, issn = {0378-4371}, doi = {10.1016/j.physa.2009.12.062}, year = {2010}, abstract = {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.}, language = {en} } @article{SchinkelMarwanDimigenetal.2009, author = {Schinkel, Stefan and Marwan, Norbert and Dimigen, Olaf and Kurths, J{\"u}rgen}, title = {Confidence bounds of recurrence-based complexity measures}, issn = {0375-9601}, doi = {10.1016/j.physleta.2009.04.045}, year = {2009}, abstract = {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.}, language = {en} } @article{BreitenbachRehfeldGoswamietal.2012, author = {Breitenbach, Sebastian Franz Martin and Rehfeld, Kira and Goswami, Bedartha and Baldini, James U. L. and Ridley, H. E. and Kennett, D. J. and Prufer, K. M. and Aquino, Valorie V. and Asmerom, Yemane and Polyak, V. J. and Cheng, Hai and Kurths, J{\"u}rgen and Marwan, Norbert}, title = {Constructing Proxy Records from Age models (COPRA)}, series = {Climate of the past : an interactive open access journal of the European Geosciences Union}, volume = {8}, journal = {Climate of the past : an interactive open access journal of the European Geosciences Union}, number = {5}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1814-9324}, doi = {10.5194/cp-8-1765-2012}, pages = {1765 -- 1779}, year = {2012}, abstract = {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.}, language = {en} } @article{SteuerZhouKurths2003, author = {Steuer, Ralf and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Constructive effects of fluctuations in genetic and biochemical regulatory systems}, issn = {0303-2647}, year = {2003}, abstract = {Biochemical and genetic regulatory systems that involve low concentrations of molecules are inherently noisy. This intrinsic stochasticity, has received considerable interest recently, leading to new insights about the sources and consequences of noise in complex systems of genetic regulation. However, most prior work was devoted to the reduction of fluctuation and the robustness of cellular function with respect to intrinsic noise. Here, we focus on several scenarios in which the inherent molecular fluctuations are not merely a nuisance, but act constructively and bring about qualitative changes in the dynamics of the system. It will be demonstrated that in many typical situations biochemical and genetic regulatory systems may utilize intrinsic noise to their advantage. (C) 2002 Elsevier Ireland Ltd. All rights reserved}, language = {en} } @article{ZaikinRosenblumLandaetal.1997, author = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen}, title = {Control of noise-induced oscillations of a pendulum with a rondomly vibrating suspension axis}, year = {1997}, language = {en} } @article{LindTitzKuhlbrodtetal.2004, author = {Lind, P. G. and Titz, Sven Holger and Kuhlbrodt, Till and Corte-Real, J. A. M. and Kurths, J{\"u}rgen and Gallas, J. A. C. and Feudel, Ulla}, title = {Coupled bistable maps : a tool to study convection parameterization in ocean models}, issn = {0218-1274}, year = {2004}, abstract = {We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells. For large diffusion our model exhibits a phase transition from convective patterns to a homogeneous state over the entire lattice. In hysteresis experiments we find staircase behavior depending on stability thresholds of local convection patterns. This nonphysical behavior is suspected to induce spurious abrupt changes in the spreading of convection in ocean models. The final steady state of convective cells depends not only on the magnitude of the advective velocity but also on its direction, implying a possible bias in the development of convective patterns. Such bias points to the need for an appropriate choice of grid geometry in ocean modeling}, language = {en} } @article{MarwanNowaczykKurthsetal.2001, author = {Marwan, Norbert and Nowaczyk, Norbert R. and Kurths, J{\"u}rgen and Thiel, Marco}, title = {Cross recurrence plot based rescaling of geological time series}, issn = {1029-7006}, year = {2001}, abstract = {The rescaling of geological data series to a geological reference time series is of major interest in many investigations. For example, geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Usually this synchronization is performed visually and by hand. Instead of using this wiggle matching by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and rescaling of geological data to a given time scale is much easier and faster than by hand.}, language = {en} } @article{MaraunKurths2004, author = {Maraun, Douglas and Kurths, J{\"u}rgen}, title = {Cross wavelet analysis: significance testing and pitfalls}, issn = {1023-5809}, year = {2004}, abstract = {In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs}, language = {en} } @article{VincentKenfackSenthilkumaretal.2010, author = {Vincent, Uchechukwu E. and Kenfack, Anatole and Senthilkumar, Dharmapuri Vijayan and Mayer, Dieter and Kurths, J{\"u}rgen}, title = {Current reversals and synchronization in coupled ratchets}, issn = {1539-3755}, doi = {10.1103/Physreve.82.046208}, year = {2010}, abstract = {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.}, language = {en} } @article{GozolchianiMoshelHausdorffetal.2006, author = {Gozolchiani, Avi and Moshel, Shay and Hausdorff, Jeffrey M. and Simon, Ely and Kurths, J{\"u}rgen and Havlin, Shlomo}, title = {Decaying of phase synchronization in parkinsonian tremor}, issn = {0378-4371}, doi = {10.1016/j.physa.2005.10.033}, year = {2006}, abstract = {We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.}, language = {en} } @article{RetzlaffBauernschmittMalbergetal.2009, author = {Retzlaff, Beatrice and Bauernschmitt, Robert and Malberg, Hagen and Brockmann, Gernot and Uhl, Christian and Lange, Ruediger and Kurths, J{\"u}rgen and Bretthauer, Georg and Wessel, Niels}, title = {Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0272}, year = {2009}, abstract = {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.}, language = {en} } @article{KimKurthsKimetal.1998, author = {Kim, G. G. and Kurths, J{\"u}rgen and Kim, S. and Cao, L. Y.}, title = {Detecting determinism in human posture control data}, year = {1998}, language = {en} } @unpublished{ThiessenhusenEspositoKurthsetal.1995, author = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank}, title = {Detection of hidden resonances in Saturn's B-ring}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618}, year = {1995}, abstract = {The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.}, language = {en} } @article{TassRosenblumWeuleetal.1998, author = {Tass, Peter and Rosenblum, Michael and Weule, J. and Kurths, J{\"u}rgen and Pikovskij, Arkadij and Volkmann, J. and Schnitzler, A. and Freund, H.-J.}, title = {Detection of n:m phase locking from noisy data : application to magnetoencephalography}, year = {1998}, abstract = {We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that}, language = {en} } @article{RomanoThielKurthsetal.2005, author = {Romano, Maria Carmen and Thiel, M. and Kurths, J{\"u}rgen and Kiss, Istvan Z. and Hudson, J. L.}, title = {Detection of synchronization for non-phase-coherent and non-stationary data}, issn = {0295-5075}, year = {2005}, abstract = {We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rossler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase- coherent and even non-stationary time series}, language = {en} } @article{KoseskaVolkovKurths2009, author = {Koseska, Aneta and Volkov, Evgenij and Kurths, J{\"u}rgen}, title = {Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators}, issn = {0295-5075}, doi = {10.1209/0295-5075/85/28002}, year = {2009}, abstract = {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.}, language = {en} } @article{SaparinKurthsGowinetal.1997, author = {Saparin, Peter and Kurths, J{\"u}rgen and Gowin, P. and Felsenberg, D.}, title = {Die quantitative Beurteilung trabecul{\"a}rer Knochenstrukturen der Lendenwirbelk{\"o}rper durch Meßmethoden der nicht-linearen Dynamik}, year = {1997}, language = {de} } @article{ZaikinKurthsSchimanskyGeier2000, author = {Zaikin, Alexei A. and Kurths, J{\"u}rgen and Schimansky-Geier, Lutz}, title = {Doubly stochastic resonance}, year = {2000}, abstract = {We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.}, language = {en} } @article{MalikZouMarwanetal.2012, author = {Malik, Nishant and Zou, Y. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Dynamical regimes and transitions in plio-pleistocene Asian monsoon}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {97}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {4}, publisher = {EDP Sciences}, address = {Mulhouse}, issn = {0295-5075}, doi = {10.1209/0295-5075/97/40009}, pages = {6}, year = {2012}, abstract = {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.}, language = {en} } @article{ZhouKurths2006, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Dynamical weights and enhanced synchronization in adaptive complex networks}, doi = {10.1103/Physrevlett.96.164102}, year = {2006}, abstract = {Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks}, language = {en} } @article{RuzickScheffczykPikovskijetal.1997, author = {Ruzick, Oliver and Scheffczyk, Christian and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Dynamics of chaos-order interface in coupled map lattices}, year = {1997}, language = {en} } @misc{MotterMatiasKurthsetal.2006, author = {Motter, Adilson E. and Matias, Manuel A. and Kurths, J{\"u}rgen and Ott, Edward}, title = {Dynamics on complex networks and applications}, series = {Physica. D, Nonlinear phenomena}, volume = {224}, journal = {Physica. D, Nonlinear phenomena}, number = {1-2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2006.09.012}, pages = {VII -- VIII}, year = {2006}, language = {en} } @article{AnishchenkoVadivasovaKopeikinetal.2001, author = {Anishchenko, Vadim S. and Vadivasova, T. E. and Kopeikin, A. S. and Kurths, J{\"u}rgen and Strelkova, G. I.}, title = {Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors}, year = {2001}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Effect of phase synchronization in driven chaotic oscillators}, year = {1997}, language = {en} } @article{ChenShangZhouetal.2009, author = {Chen, Maoyin and Shang, Yun and Zhou, Changsong and Wu, Ye and Kurths, J{\"u}rgen}, title = {Enhanced synchronizability in scale-free networks}, issn = {1054-1500}, doi = {10.1063/1.3062864}, year = {2009}, abstract = {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.}, language = {en} } @article{MotterZhouKurths2005, author = {Motter, Adilson E. and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Enhancing complex-network synchronization}, issn = {0295-5075}, year = {2005}, abstract = {Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in weighted networks with asymmetric coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically enhanced and may become positively correlated with heterogeneity, while the overall cost involved in the network coupling is significantly reduced as compared to the case of unwcighted coupling}, language = {en} } @article{MarwanSchwarzKurthsetal.2000, author = {Marwan, Norbert and Schwarz, Udo and Kurths, J{\"u}rgen and Strecker, Manfred}, title = {ENSO Impact on landslide generation in northwestern Argentina}, issn = {1029-7006}, year = {2000}, abstract = {Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Quantitative analysis of cross recurrence plots were developed to compare the influence of the El Nino/Southern Oscillation (ENSO) on present and past rainfall variations. This analysis has shown the stronger influence of NE trades in the location of landslide deposits in the intra-andean basin and valleys, what caused a higher contrast between summer and winter rainfall and an increasing of precipitation in La Nina years. This is believed to reduce thresholds for landslide generation in the arid to semiarid intra-andean basins and valleys.}, language = {en} } @article{WesselSchumannWesseletal.2000, author = {Wessel, Niels and Schumann, Agnes and Wessel, Niels and Schumann, Agnes and Schirdewan, Alexander and Voss, Andreas and Kurths, J{\"u}rgen}, title = {Entropy measures in heart rate variability data}, year = {2000}, language = {en} } @article{EbelingMolgedeyKurthsetal.2002, author = {Ebeling, Werner and Molgedey, Lutz and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Entropy, complexity, predictability, and data analysis of time series and letter sequences}, isbn = {3-540-41324-3}, year = {2002}, abstract = {The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.}, language = {en} } @article{MaraunKurths2005, author = {Maraun, Douglas and Kurths, J{\"u}rgen}, title = {Epochs of phase coherence between El Nino/Southern Oscillation and Indian monsoon}, issn = {0094-8276}, year = {2005}, abstract = {We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We study the difference of the phase dynamics between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. We identify distinct epochs, especially two intervals of phase coherence, 1886 - 1908 and 1964 - 1980, corroborating earlier findings from a new point of view. A significance test shows that the coherence is very unlikely to be the result of stochastic fluctuations. We also detect so far unknown periods of coupling which are invisible to linear methods. These findings suggest that the decreasing correlation during the last decades might be a typical epoch of the ENSO/ Monsoon system having occurred repeatedly. The high time resolution of the method enables us to present an interpretation of how volcanic radiative forcing could cause the coupling}, language = {en} } @article{SchwacheKurthsMitschkeetal.1999, author = {Schwache, A. and Kurths, J{\"u}rgen and Mitschke, F. and Voss, Henning U.}, title = {Equations of motion from chaotic data : a driven optical fiber ring resonator}, year = {1999}, language = {en} } @article{ThielRomanoReadetal.2004, author = {Thiel, M. and Romano, Maria Carmen and Read, P. L. and Kurths, J{\"u}rgen}, title = {Estimation of dynamical invariants without embedding by recurrence plots}, issn = {1054-1500}, year = {2004}, abstract = {In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics}, language = {en} } @article{RaabKurths2001, author = {Raab, Corinna and Kurths, J{\"u}rgen}, title = {Estimation of Large-Scale Dimension Densities}, year = {2001}, abstract = {We propose a technique to calculate large-scale dimension densities in both higher-dimensional spatio-temporal systems and low-dimensional systems from only a few data points, where known methods usually have an unsatisfactory scaling behavior. This is mainly due to boundary and finite size effects. With our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate. This straightforward approach is basing on rather general assumptions. So even weak coherent structures obtained from small spatial couplings can be detected with this method, what is impossible by using the Lyapunov-dimension density. We demonstrate the efficiency of our technique for coupled logistic maps, coupled tent maps, the Lorenz-attractor and the Roessler-attractor.}, language = {en} } @article{SitzSchwarzKurthsetal.2002, author = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Voss, Henning U.}, title = {Estimation of parameters and unobserved components for nonlinear systems from noisy time series}, year = {2002}, abstract = {We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.}, language = {en} } @article{GoswamiHeitzigRehfeldetal.2014, author = {Goswami, Bedartha and Heitzig, Jobst and Rehfeld, Kira and Marwan, Norbert and Anoop, Ambili and Prasad, Sushma and Kurths, J{\"u}rgen}, title = {Estimation of sedimentary proxy records together with associated uncertainty}, series = {Nonlinear processes in geophysics}, volume = {21}, journal = {Nonlinear processes in geophysics}, number = {6}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1023-5809}, doi = {10.5194/npg-21-1093-2014}, pages = {1093 -- 1111}, year = {2014}, abstract = {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.}, language = {en} } @article{WesselVossKurthsetal.2000, author = {Wessel, Niels and Voss, Andreas and Kurths, J{\"u}rgen and Schirdewan, Alexander and Hnatkova, Katarina and Malik, Marek}, title = {Evaluation of renormalised entropy for risk stratification using heart rate variability data}, year = {2000}, abstract = {Standard time and frequency parameters of heart rate variability (HRV) describe only linear and periodic behaviour, whereas more complex relationships cannot be recognised. A method that may be capable of assessing more complex properties is the non-linear measure of 'renormalised entropy.' A new concept of the method, RE(AR), has been developed, based on a non-linear renormalisation of autoregressive spectral distributions. To test the hypothesis that renormalised entropy may improve the result of high-risk stratification after myocardial infarction, it is applied to a clinical pilot study (41 subjects) and to prospective data of the St George's Hospital post- infarction database (572 patients). The study shows that the new RE(AR) method is more reproducible and more stable in time than a previously introduced method (p<0.001). Moreover, the results of the study confirm the hypothesis that on average, the survivors have negative values of RE(AR) (-0.11+/-0.18), whereas the non-survivors have positive values (0.03+/-0.22, p<0.01). Further, the study shows that the combination of an HRV triangular index and RE(AR) leads to a better prediction of sudden arrhythmic death than standard measurements of HRV. In summary, the new RE(AR) method is an independent measure in HRV analysis that may be suitable for risk stratification in patients after myocardial infarction.}, language = {en} } @article{WuZhouXiaoetal.2010, author = {Wu, Ye Wu and Zhou, Changsong and Xiao, Jinghua and Kurths, J{\"u}rgen and Schellnhuber, Hans Joachim}, title = {Evidence for a bimodal distribution in human communication}, issn = {0027-8424}, doi = {10.1073/pnas.1013140107}, year = {2010}, abstract = {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.}, language = {en} } @article{DanaBlasiusKurths2006, author = {Dana, Syamal Kumar and Blasius, Bernd and Kurths, J{\"u}rgen}, title = {Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators}, issn = {1054-1500}, doi = {10.1063/1.2197168}, year = {2006}, abstract = {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}, language = {en} } @article{BoersBookhagenMarengoetal.2015, author = {Boers, Niklas and Bookhagen, Bodo and Marengo, Jose and Marwan, Norbert and von Storch, Jin-Song and Kurths, J{\"u}rgen}, title = {Extreme Rainfall of the South American Monsoon System: A Dataset Comparison Using Complex Networks}, series = {Journal of climate}, volume = {28}, journal = {Journal of climate}, number = {3}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0894-8755}, doi = {10.1175/JCLI-D-14-00340.1}, pages = {1031 -- 1056}, year = {2015}, abstract = {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.}, language = {en} } @article{ErogluMarwanPrasadetal.2014, author = {Eroglu, Deniz and Marwan, Norbert and Prasad, Sushma and Kurths, J{\"u}rgen}, title = {Finding recurrence networks' threshold adaptively for a specific time series}, series = {Nonlinear processes in geophysics}, volume = {21}, journal = {Nonlinear processes in geophysics}, number = {6}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1023-5809}, doi = {10.5194/npg-21-1085-2014}, pages = {1085 -- 1092}, year = {2014}, abstract = {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.}, language = {en} } @article{SurovyatkinaKravtsovKurths2005, author = {Surovyatkina, E. D. and Kravtsov, Y. A. and Kurths, J{\"u}rgen}, title = {Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking}, issn = {1539-3755}, year = {2005}, abstract = {We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed}, language = {en} } @article{BoveBoccalettiBragardetal.2004, author = {Bove, I. and Boccaletti, Stefano and Bragard, Jean and Kurths, J{\"u}rgen and Mancini, H.}, title = {Frequency entrainment of nonautonomous chaotic oscillators}, year = {2004}, abstract = {We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty}, language = {en} } @article{VolkovUllnerZaikinetal.2003, author = {Volkov, E. I. and Ullner, Ekkehard and Zaikin, Alexei A. and Kurths, J{\"u}rgen}, title = {Frequency-dependent stochastic resonance in inhibitory coupled excitable systems}, issn = {1063-651X}, year = {2003}, abstract = {We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations}, language = {en} } @article{RosenblumPikovskijKurths1997, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {From Phase to Lag Synchronization in Coupled Chaotic Oscillators}, year = {1997}, abstract = {We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.}, language = {en} } @article{ThielRomanoKurthsetal.2008, author = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold}, title = {Generating surrogates from recurrences}, issn = {1364-503X}, year = {2008}, abstract = {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.}, language = {en} } @misc{ThielRomanoKurthsetal.2006, author = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold}, title = {Generating Surrogates from Recurrences}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56906}, year = {2006}, abstract = {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 one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.}, language = {en} } @article{PereiraBaptistaReyesetal.2006, author = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo Bussotti and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen}, title = {Global bifurcation destroying the experimental torus T-2}, doi = {10.1103/Physreve.73.017201}, year = {2006}, abstract = {We show experimentally the scenario of a two-frequency torus T-2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior}, language = {en} } @article{SureshSenthilkumarLakshmananetal.2010, author = {Suresh, R. and Senthilkumar, Dharmapuri Vijayan and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen}, title = {Global phase synchronization in an array of time-delay systems}, issn = {1539-3755}, doi = {10.1103/Physreve.82.016215}, year = {2010}, abstract = {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.}, language = {en} } @article{ZamoraLopezZhouKurths2009, author = {Zamora-Lopez, Gorka and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Graph analysis of cortical networks reveals complex anatomical communication substrate}, issn = {1054-1500}, doi = {10.1063/1.3089559}, year = {2009}, abstract = {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.}, language = {en} } @article{RosenblumKurthsSchaeferetal.1998, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten and Abel, Hans-Henning}, title = {Heartbeat synchronized with ventilation}, year = {1998}, language = {en} } @article{ZhouZemanovaZamoraetal.2006, author = {Zhou, Changsong and Zemanova, Lucia and Zamora, Gorka and Hilgetag, Claus C. and Kurths, J{\"u}rgen}, title = {Hierarchical organization unveiled by functional connectivity in complex brain networks}, series = {Physical review letters}, volume = {97}, journal = {Physical review letters}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.97.238103}, pages = {4}, year = {2006}, abstract = {How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.}, language = {en} } @article{ZhouKurths2006, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Hierarchical synchronization in complex networks with heterogeneous degrees}, issn = {1054-1500}, doi = {10.1063/1.2150381}, year = {2006}, abstract = {We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics}, language = {en} } @article{CiemerBoersHirotaetal.2019, author = {Ciemer, Catrin and Boers, Niklas and Hirota, Marina and Kurths, J{\"u}rgen and M{\"u}ller-Hansen, Finn and Oliveira, Rafael S. and Winkelmann, Ricarda}, title = {Higher resilience to climatic disturbances in tropical vegetation exposed to more variable rainfall}, series = {Nature geoscience}, volume = {12}, journal = {Nature geoscience}, number = {3}, publisher = {Nature Publ. Group}, address = {New York}, issn = {1752-0894}, doi = {10.1038/s41561-019-0312-z}, pages = {174 -- 179}, year = {2019}, abstract = {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.}, language = {en} } @article{GoswamiMarwanFeulneretal.2013, author = {Goswami, Bedartha and Marwan, Norbert and Feulner, Georg and Kurths, J{\"u}rgen}, title = {How do global temperature drivers influence each other?}, series = {European physical journal special topics}, volume = {222}, journal = {European physical journal special topics}, number = {3-4}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2013-01889-8}, pages = {861 -- 873}, year = {2013}, abstract = {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.}, language = {en} } @article{ThielRomanoKurths2004, author = {Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen}, title = {How much information is contained in a recurrence plot?}, issn = {0375-9601}, year = {2004}, abstract = {Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved}, language = {en} } @article{WuZhouChenetal.2010, author = {Wu, Ye and Zhou, Changsong and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen}, title = {Human comment dynamics in on-line social systems}, issn = {0378-4371}, doi = {10.1016/j.physa.2010.08.049}, year = {2010}, abstract = {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.}, language = {en} } @article{RomanoThielKurthsetal.2009, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Mergenthaler, Konstantin and Engbert, Ralf}, title = {Hypothesis test for synchronization : twin surrogates revisited}, issn = {1054-1500}, doi = {10.1063/1.3072784}, year = {2009}, abstract = {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.}, language = {en} } @article{DongesDonnerRehfeldetal.2011, author = {Donges, Jonathan and Donner, Reik Volker and Rehfeld, Kira and Marwan, Norbert and Trauth, Martin H. and Kurths, J{\"u}rgen}, title = {Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis}, series = {Nonlinear processes in geophysics}, volume = {18}, journal = {Nonlinear processes in geophysics}, number = {5}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1023-5809}, doi = {10.5194/npg-18-545-2011}, pages = {545 -- 562}, year = {2011}, abstract = {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.}, language = {en} } @article{LandaZaikinUshakovetal.2000, author = {Landa, Polina S. and Zaikin, Alexei A. and Ushakov, V. G. and Kurths, J{\"u}rgen}, title = {Influence of additive noise on transitions in nonlinear systems}, year = {2000}, abstract = {The effect of additive noise on transitions in nonlinear systems far from equilibrium is studied. It is shown that additive noise in itself can induce a hidden phase transition, which is similar to the transition induced by multiplicative noise in a nonlinear oscillator [P. Landa and A. Zaikin, Phys. Rev. E 54, 3535 (1996)]. Investigation of different nonlinear models that demonstrate phase transitions induced by multiplicative noise shows that the influence of additive noise upon such phase transitions can be crucial: additive noise can either blur such a transition or stabilize noise-induced oscillations.}, language = {en} } @article{OrgisBrandSchwarzetal.2009, author = {Orgis, Thomas and Brand, Sascha and Schwarz, Udo and Handorf, D{\"o}rthe and Dethloff, Klaus and Kurths, J{\"u}rgen}, title = {Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model}, issn = {1951-6355}, doi = {10.1140/epjst/e2009-01105-8}, year = {2009}, abstract = {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.}, language = {en} } @article{BaptistaZhouKurths2006, author = {Baptista, Murilo da Silva and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Information transmission in phase synchronous chaotic arrays}, issn = {0256-307X}, doi = {10.1088/0256-307X/23/3/010}, year = {2006}, abstract = {We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize}, language = {en} } @article{HempelKoseskaKurthsetal.2011, author = {Hempel, Stefan and Koseska, Aneta and Kurths, J{\"u}rgen and Nikoloski, Zoran}, title = {Inner composition alignment for inferring directed networks from short time series}, series = {Physical review letters}, volume = {107}, journal = {Physical review letters}, number = {5}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.107.054101}, pages = {4}, year = {2011}, abstract = {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.}, language = {en} } @article{RusconiVallerianiDunlopetal.2009, author = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard}, title = {Insights into the control of trabecular bone remodelling obtained by a Markov model}, issn = {8756-3282}, doi = {10.1016/j.bone.2009.03.467}, year = {2009}, language = {en} } @article{SteuerKurthsFiehnetal.2003, author = {Steuer, Ralf and Kurths, J{\"u}rgen and Fiehn, Oliver and Weckwerth, Wolfram}, title = {Interpreting correlations in metabolomic networks}, issn = {0300-5127}, year = {2003}, abstract = {Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. in this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways}, language = {en} } @book{RosenblumSchaeferAbeletal.1997, author = {Rosenblum, Michael and Sch{\"a}fer, Carsten and Abel, Hans-Henning and Kurths, J{\"u}rgen}, title = {Interrelationship of Parasympathetic Innervation of the Sinoatrial Node and the Atrioventricular Node of Human Heart}, issn = {1120-1797}, year = {1997}, language = {en} } @article{FeudelWittGellertetal.2005, author = {Feudel, Fred and Witt, Annette and Gellert, Marcus and Kurths, J{\"u}rgen and Grebogi, Celso and Sanjuan, Miguel Angel Fernandez}, title = {Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos}, year = {2005}, abstract = {We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved}, language = {en} } @article{HellandGapelyukSuhrbieretal.2010, author = {Helland, Vanessa Carolina Figuera and Gapelyuk, Andrej and Suhrbier, Alexander and Riedl, Maik and Penzel, Thomas and Kurths, J{\"u}rgen and Wessel, Niels}, title = {Investigation of an automatic sleep stage classification by means of multiscorer hypnogram}, issn = {0026-1270}, doi = {10.3414/Me09-02-0052}, year = {2010}, abstract = {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}, language = {en} }