@book{RosenblumKurths1995,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen},
  title     = {A model of neural control of heart rate},
  series = {Preprint NLD},
  volume    = {12},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {22 S.},
  year      = {1995},
  language  = {en}
}
@article{OzturkMalikCheungetal.2019,
  author    = {Ozturk, Ugur and Malik, Nishant and Cheung, Kevin and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {A network-based comparative study of extreme tropical and frontal storm rainfall over Japan},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {53},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  number    = {1-2},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-018-4597-1},
  pages     = {521 -- 532},
  year      = {2019},
  abstract  = {Frequent and intense rainfall events demand innovative techniques to better predict the extreme rainfall dynamics. This task requires essentially the assessment of the basic types of atmospheric processes that trigger extreme rainfall, and then to examine the differences between those processes, which may help to identify key patterns to improve predictive algorithms. We employ tools from network theory to compare the spatial features of extreme rainfall over the Japanese archipelago and surrounding areas caused by two atmospheric processes: the Baiu front, which occurs mainly in June and July (JJ), and the tropical storms from August to November (ASON). We infer from complex networks of satellite-derived rainfall data, which are based on the nonlinear correlation measure of event synchronization. We compare the spatial scales involved in both systems and identify different regions which receive rainfall due to the large spatial scale of the Baiu and tropical storm systems. We observed that the spatial scales involved in the Baiu driven rainfall extremes, including the synoptic processes behind the frontal development, are larger than tropical storms, which even have long tracks during extratropical transitions. We further delineate regions of coherent rainfall during the two seasons based on network communities, identifying the horizontal (east-west) rainfall bands during JJ over the Japanese archipelago, while during ASON these bands align with the island arc of Japan.},
  language  = {en}
}
@article{GoswamiShekatkarRheinwaltetal.2015,
  author    = {Goswami, Bedartha and Shekatkar, Snehal M. and Rheinwalt, Aljoscha and Ambika, G. and Kurths, J{\"u}rgen},
  title     = {A random interacting network model for complex networks},
  series = {Scientific reports},
  volume    = {5},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep18183},
  pages     = {10},
  year      = {2015},
  abstract  = {We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.},
  language  = {en}
}
@article{PereiraBaptistaReyesetal.2009,
  author    = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo B. and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen},
  title     = {A scenario for torus T-2 destruction via a global bifurcation},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2007.06.115},
  year      = {2009},
  abstract  = {We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T-2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type- if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.},
  language  = {en}
}
@misc{GoswamiBoersRheinwaltetal.2018,
  author    = {Goswami, Bedartha and Boers, Niklas and Rheinwalt, Aljoscha and Marwan, Norbert and Heitzig, Jobst and Breitenbach, Sebastian Franz Martin and Kurths, J{\"u}rgen},
  title     = {Abrupt transitions in time series with uncertainties},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {576},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42311},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-423111},
  pages     = {10},
  year      = {2018},
  abstract  = {Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Nino-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.},
  language  = {en}
}
@article{GoswamiBoersRheinwaltetal.2018,
  author    = {Goswami, Bedartha and Boers, Niklas and Rheinwalt, Aljoscha and Marwan, Norbert and Heitzig, Jobst and Breitenbach, Sebastian Franz Martin and Kurths, J{\"u}rgen},
  title     = {Abrupt transitions in time series with uncertainties},
  series = {Nature Communications},
  volume    = {9},
  journal   = {Nature Communications},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2041-1723},
  doi       = {10.1038/s41467-017-02456-6},
  pages     = {10},
  year      = {2018},
  abstract  = {Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Ni{\~n}o-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.},
  language  = {en}
}
@article{ZaikinKurths2000,
  author    = {Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Additive noise and noise-induced nonequilibrium phase transitions},
  isbn      = {1-563-96826-6},
  year      = {2000},
  language  = {en}
}
@article{ZaikinKurths2001,
  author    = {Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Additive noise in noise-induced nonequilibrium transitions},
  issn      = {1054-1500},
  year      = {2001},
  language  = {en}
}
@article{PortaDiRienzoWesseletal.2009,
  author    = {Porta, Alberto and Di Rienzo, Marco and Wessel, Niels and Kurths, J{\"u}rgen},
  title     = {Addressing the complexity of cardiovascular regulation},
  issn      = {1364-503X},
  doi       = {10.1098/rsta.2008.0292},
  year      = {2009},
  language  = {en}
}
@article{ParkRosenblumKurthsetal.1999,
  author    = {Park, Eun Hyoung and Rosenblum, Michael and Kurths, J{\"u}rgen and Zaks, Michael A.},
  title     = {Alternating locking ratios in imperfect phase synchronization},
  year      = {1999},
  language  = {en}
}
@article{KolodnerAbelKurthsetal.1999,
  author    = {Kolodner, P. and Abel, Markus and Kurths, J{\"u}rgen and Voss, Henning U.},
  title     = {Amplitude equations from spatiotemporal binary-fluid convection data},
  year      = {1999},
  language  = {en}
}
@article{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {An approach to multivariate phase synchronization analysis and its application to event-related potentials},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields},
  language  = {en}
}
@misc{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {An approach to multivariate phase synchronization analysis and its application to event-related potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20106},
  year      = {2004},
  abstract  = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.},
  language  = {en}
}
@misc{CiemerRehmKurthsetal.2020,
  author    = {Ciemer, Catrin and Rehm, Lars and Kurths, J{\"u}rgen and Donner, Reik Volker and Winkelmann, Ricarda and Boers, Niklas},
  title     = {An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {9},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-52586},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-525863},
  pages     = {12},
  year      = {2020},
  abstract  = {Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.},
  language  = {en}
}
@article{CiemerRehmKurthsetal.2020,
  author    = {Ciemer, Catrin and Rehm, Lars and Kurths, J{\"u}rgen and Donner, Reik Volker and Winkelmann, Ricarda and Boers, Niklas},
  title     = {An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures},
  series = {Environmental Research Letters},
  volume    = {15},
  journal   = {Environmental Research Letters},
  number    = {9},
  publisher = {IOP - Institute of Physics Publishing},
  address   = {Bristol},
  pages     = {10},
  year      = {2020},
  abstract  = {Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.},
  language  = {en}
}
@article{ZakharovaKurthsVadivasovaetal.2011,
  author    = {Zakharova, Anna and Kurths, J{\"u}rgen and Vadivasova, Tatyana and Koseska, Aneta},
  title     = {Analysing dynamical behavior of cellular networks via stochastic bifurcations},
  series = {PLoS one},
  volume    = {6},
  journal   = {PLoS one},
  number    = {5},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0019696},
  pages     = {12},
  year      = {2011},
  abstract  = {The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.},
  language  = {en}
}
@article{PavlovAnisimovSemyachkinaGlushkovskayaetal.2009,
  author    = {Pavlov, Alexey N. and Anisimov, A. A. and Semyachkina-Glushkovskaya, Oxana V. and Matasova, E. G. and Kurths, J{\"u}rgen},
  title     = {Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform},
  issn      = {0967-3334},
  doi       = {10.1088/0967-3334/30/7/013},
  year      = {2009},
  abstract  = {We study gender-related particularities in cardiovascular responses to stress and nitric oxide (NO) deficiency in rats using HR, mean arterial pressure (MAP) and a proposed wavelet-based approach. Blood pressure dynamics is analyzed: (1) under control conditions, (2) during immobilization stress and recovery and (3) during nitric oxide blockade by N-G-nitro-L-arginine-methyl ester (L-NAME). We show that cardiovascular sensitivity to stress and NO deficiency depends upon gender. Actually, in females the chronotropic effect of stress is more pronounced, while the pressor effect is weakened compared with males. We conclude that females demonstrate more favorable patterns of cardiovascular responses to stress and more effective NO control of cardiovascular activity than males.},
  language  = {en}
}
@article{KomalapriyaRomanoBlascoThieletal.2009,
  author    = {Komalapriya, Chandrasekaran and Romano Blasco, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Simonotto, Jennifer and Furman, Michael and Ditto, William L. and Carney, Paul R.},
  title     = {Analysis of high-resulution microelectrode EEG recordings in an animal model of spontaneous limbic seizures},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127409023226},
  year      = {2009},
  language  = {en}
}
@article{SchwarzBenzKurthsetal.1993,
  author    = {Schwarz, udo and Benz, Arnold O. and Kurths, J{\"u}rgen and Witt, Annette},
  title     = {Analysis of solar spike events by means of symbolic dynamics methods},
  issn      = {004-6361},
  year      = {1993},
  abstract  = {Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter.},
  language  = {en}
}
@article{MalikBookhagenMarwanetal.2012,
  author    = {Malik, Nishant and Bookhagen, Bodo and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {39},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  number    = {3-4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-011-1156-4},
  pages     = {971 -- 987},
  year      = {2012},
  abstract  = {We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June-September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades.},
  language  = {en}
}
@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}
}