TY - JOUR A1 - Anishchenko, Vadim S. A1 - Nikolaev, S A1 - Kurths, Jürgen T1 - Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions N2 - We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.056202 SN - 1539-3755 ER - TY - JOUR A1 - Agarwal, Ankit A1 - Maheswaran, Rathinasamy A1 - Marwan, Norbert A1 - Caesar, Levke A1 - Kurths, Jürgen T1 - Wavelet-based multiscale similarity measure for complex networks JF - The European physical journal : B, Condensed matter and complex systems N2 - In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales. KW - Statistical and Nonlinear Physics Y1 - 2018 U6 - https://doi.org/10.1140/epjb/e2018-90460-6 SN - 1434-6028 SN - 1434-6036 VL - 91 IS - 11 PB - Springer CY - New York ER - TY - JOUR A1 - Kliem, Bernhard A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Dennis, Brian A1 - Schwartz, Richard A1 - Aschwanden, Markus J. T1 - Wavelet analysis of solar flare hard X-ray Y1 - 1998 SN - 0004-637x ER - TY - JOUR A1 - Maheswaran, Rathinasamy A1 - Agarwal, Ankit A1 - Sivakumar, Bellie A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Wavelet analysis of precipitation extremes over India and teleconnections to climate indices JF - Stochastic Environmental Research and Risk Assessment N2 - Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Nino 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Nino 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region. KW - Extreme precipitation KW - Teleconnection patterns KW - Wavelets KW - Partial wavelet coherence KW - India Y1 - 2019 U6 - https://doi.org/10.1007/s00477-019-01738-3 SN - 1436-3240 SN - 1436-3259 VL - 33 IS - 11-12 SP - 2053 EP - 2069 PB - Springer CY - New York ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - López, L A1 - Baltanás, J. P. A1 - Kurths, Jürgen A1 - Sanjuan, Miguel Angel Fernández T1 - Vibrational resonance in noise-induced structure N2 - We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise- induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit. Y1 - 2002 UR - http://link.aps.org/abstract/PRE/v66/e011106 ER - TY - JOUR A1 - Gandhimathi, V. M. A1 - Rajasekar, S. A1 - Kurths, Jürgen T1 - Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators JF - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved. KW - vibrational resonance KW - low-frequency force KW - high-frequency force KW - stochastic resonance KW - noise KW - mean residence time Y1 - 2006 U6 - https://doi.org/10.1016/j.physleta.2006.08.051 SN - 0375-9601 VL - 360 IS - 2 SP - 279 EP - 286 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Viana, R. L. A1 - Grebogi, Celso A1 - Pinto, Seds A1 - Lopes, S. R. A1 - Batista, A. M. A1 - Kurths, Jürgen T1 - Validity of numerical trajectories in the synchronization transition of complex systems N2 - We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties Y1 - 2003 SN - 1063-651X ER - TY - JOUR A1 - Baptista, Murilo da Silva A1 - Pereira, Tiago A1 - Kurths, Jürgen T1 - Upper bounds in phase synchronous weak coherent chaotic attractors N2 - An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/01672789 U6 - https://doi.org/10.1016/j.physd.2006.02.007 SN - 0167-2789 ER - TY - JOUR A1 - Kurths, Jürgen A1 - Agarwal, Ankit A1 - Shukla, Roopam A1 - Marwan, Norbert A1 - Maheswaran, Rathinasamy A1 - Caesar, Levke A1 - Krishnan, Raghavan A1 - Merz, Bruno T1 - Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach JF - Nonlinear processes in geophysics N2 - A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting. Y1 - 2019 U6 - https://doi.org/10.5194/npg-26-251-2019 SN - 1023-5809 SN - 1607-7946 VL - 26 IS - 3 SP - 251 EP - 266 PB - Copernicus CY - Göttingen ER - TY - GEN A1 - Hempel, Sabrina A1 - Koseska, Aneta A1 - Nikoloski, Zoran A1 - Kurths, Jürgen T1 - Unraveling gene regulatory networks from time-resolved gene expression data BT - a measures comparison study N2 - Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 371 KW - unferring cellular networks KW - mutual information KW - Escherichia-coli KW - cluster-analysis KW - series KW - algorithms KW - inference KW - models KW - recognition KW - variables Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400924 ER - TY - JOUR A1 - Zhou, Changsong A1 - Motter, Adilson E. A1 - Kurths, Jürgen T1 - Universality in the synchronization of weighted random networks N2 - Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters Y1 - 2006 UR - http://prl.aps.org/pdf/PRL/v96/i3/e034101 U6 - https://doi.org/10.1103/Physrevlett.96.034101 ER - TY - GEN A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin T1 - Twin Surrogates to Test for Complex Synchronisation N2 - We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - paper 264 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57231 ER - TY - JOUR A1 - Zhang, H. A1 - Hu, B. A1 - Hu, G. A1 - Ouyang, Q. A1 - Kurths, Jürgen T1 - Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Laundau equation Y1 - 2002 ER - TY - JOUR A1 - Heuer, Axel A1 - Schultheiss, J. A1 - Hodgson, N. A1 - Kurths, Jürgen A1 - Menzel, Ralf A1 - Raab, Volker T1 - Transverse effects in phase conjugate laser mirrors based on stimulated brillouin scattering Y1 - 1999 ER - TY - JOUR A1 - Hassan, M. K. A1 - Kurths, Jürgen T1 - Transition from random to ordered fractals in fragmentation of particles in an open system Y1 - 2001 ER - TY - JOUR A1 - Popovych, Orest A1 - Maistrenko, Yu A1 - Mosekilde, Erik A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Transcritical riddling in a system of coupled maps N2 - The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state. Y1 - 2001 ER - TY - JOUR A1 - Popovych, Orest A1 - Maistrenko, Yu A1 - Mosekilde, Erik A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Transcritical loss of synchronization in coupled chaotic systems Y1 - 2000 ER - TY - JOUR A1 - Braun, Robert A1 - Feudel, Fred A1 - Gebogi, C. A1 - Kurths, Jürgen A1 - Witt, Annette T1 - Tracer dynamics in a flow of driven vortices Y1 - 1999 ER - TY - JOUR A1 - Stolbova, Veronika A1 - Surovyatkina, Elena A1 - Bookhagen, Bodo A1 - Kurths, Jürgen T1 - Tipping elements of the Indian monsoon: Prediction of onset and withdrawal JF - Geophysical research letters N2 - Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation. Y1 - 2016 U6 - https://doi.org/10.1002/2016GL068392 SN - 0094-8276 SN - 1944-8007 VL - 43 SP - 3982 EP - 3990 PB - American Geophysical Union CY - Washington ER - TY - GEN A1 - Koseska, Aneta A1 - Zaikin, Alexey A1 - Kurths, Jürgen A1 - García-Ojalvo, Jordi T1 - Timing cellular decision making under noise via cell-cell communication N2 - Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 148 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45260 ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Kurths, Jürgen A1 - Osipov, Grigory V. T1 - The synchronization of chaotic systems Y1 - 2002 ER - TY - JOUR A1 - Palus, Milan A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Seehafer, Norbert A1 - Novotna, Dagmar A1 - Charvatova, Ivanka T1 - The solar activity cycle is weakly synchronized with the solar inertial motion N2 - We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM. Y1 - 2007 UR - http://www.sciencedirect.com/ science?_ob=GatewayURL&_method=citationSearch&_urlVersion=4&_origin=SDVIALERTHTML&_version=1&_uoikey=B6TVM-4MYVG5S- 1&md5=92d1fc7094be5195504f17e1afb4f0d1 U6 - https://doi.org/10.1016/j.physleta.2007.01.039 ER - TY - JOUR A1 - Ziehmann, Christine A1 - Smith, L. A1 - Kurths, Jürgen T1 - The bootstrap and lyapunov exponents in deterministic chaos Y1 - 1999 ER - TY - JOUR A1 - Witt, Annette A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij T1 - Testing stationarity in time series Y1 - 1998 ER - TY - JOUR A1 - Engbert, Ralf A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Testing for unstable periodic orbits to characterize spatiotemporal dynamics Y1 - 1998 ER - TY - JOUR A1 - Allefeld, Carsten A1 - Kurths, Jürgen T1 - Testing for phase synchronization N2 - We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series Y1 - 2004 SN - 0218-1274 ER - TY - GEN A1 - Allefeld, Carsten A1 - Kurths, Jürgen T1 - Testing for phase synchronization N2 - We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 071 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20091 ER - TY - JOUR A1 - Voss, Henning U. A1 - Kurths, Jürgen T1 - Test for nonlinear dynamical behavior in symbol sequences Y1 - 1998 ER - TY - JOUR A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Engbert, Ralf A1 - Rosenblum, Michael A1 - Kurths, Jürgen A1 - Kliegl, Reinhold T1 - Tempo-induced transitions in polyrhythmic hand movements N2 - We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components. Y1 - 1997 ER - TY - INPR A1 - Engbert, Ralf A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Rosenblum, Mikhael A1 - Kurths, Jürgen A1 - Kliegl, Reinhold T1 - Tempo-induced transitions in polyrhythmic hand movements N2 - We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components. T3 - NLD Preprints - 41 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14380 ER - TY - JOUR A1 - Koseska, Aneta A1 - Volkov, Evgenii A1 - Kurths, Jürgen T1 - Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits JF - Physica scripta : an international journal for experimental and theoretical physics N2 - Synthetic biology is a relatively new research discipline that combines standard biology approaches with the constructive nature of engineering. Thus, recent efforts in the field of synthetic biology have given a perspective to consider cells as 'programmable matter'. Here, we address the possibility of using synthetic circuits to control protein dynamics. In particular, we show how intercellular communication and stochasticity can be used to manipulate the dynamical behavior of a population of coupled synthetic units and, in this manner, finely tune the expression of specific proteins of interest, e.g. in large bioreactors. Y1 - 2011 U6 - https://doi.org/10.1088/0031-8949/84/04/045007 SN - 0031-8949 VL - 84 IS - 4 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Kitajima, H. A1 - Kurths, Jürgen T1 - Synchronized firing of FitzHugh-Nagumo neurons by noise N2 - We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. (C) 2005 American Institute of Physics Y1 - 2005 SN - 1054-1500 ER - TY - JOUR A1 - Osipov, Grigory V. A1 - Ivanchenko, Mikhail V. A1 - Kurths, Jürgen A1 - Hu, B. T1 - Synchronized chaotic intermittent and spiking behavior in coupled map chains N2 - We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Ivanchenko, Mikhail V. A1 - Osipov, Grigory V. A1 - Shalfeev, V. D. A1 - Kurths, Jürgen T1 - Synchronization of two non-scalar-coupled limit-cycle oscillators N2 - Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved Y1 - 2004 ER - TY - JOUR A1 - Montbrio, Ernest A1 - Kurths, Jürgen A1 - Blasius, Bernd T1 - Synchronization of two interacting populations of oscillators N2 - We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/pre3.pdf ER - TY - JOUR A1 - Meucci, Riccardo A1 - Salvadori, Francesco A1 - Ivanchenko, Mikhail V. A1 - Al Naimee, Kais A1 - Zhou, Chansong A1 - Arecchi, Fortunato Tito A1 - Boccaletti, Stefano A1 - Kurths, Jürgen T1 - Synchronization of spontaneous bursting in a CO2 laser JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling. Y1 - 2006 U6 - https://doi.org/10.1103/PhysRevE.74.066207 SN - 2470-0045 SN - 2470-0053 VL - 74 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Li, Changpin A1 - Sun, Weigang A1 - Kurths, Jürgen T1 - Synchronization of complex dynamical networks with time delays N2 - In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2005.07.007 SN - 0378-4371 ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Valladares, D. L. A1 - Kurths, Jürgen T1 - Synchronization of chaotic structurally nonequivalent systems Y1 - 2000 ER - TY - JOUR A1 - Huang, Tingwen A1 - Chen, Guanrong A1 - Kurths, Jürgen T1 - Synchronization of chaotic of chaotic systems with time-varying coupöing delays JF - Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations N2 - In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation in equalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method. KW - Synchronization KW - Chaotic System KW - Time-varying Delay Y1 - 2011 U6 - https://doi.org/10.3934/dcdsb.2011.16.1071 SN - 1531-3492 VL - 16 IS - 4 SP - 1071 EP - 1082 PB - American Institute of Mathematical Sciences CY - Springfield ER - TY - JOUR A1 - Rosenblum, Michael A1 - Abel, Hans-Henning A1 - Kurths, Jürgen A1 - Schäfer, Carsten T1 - Synchronization in the human cardiorespiratory system Y1 - 1999 ER - TY - JOUR A1 - Rosenblum, Michael A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij A1 - Schafer, C. A1 - Tass, Peter A1 - Abel, Hans-Henning T1 - Synchronization in Noisy Systems and Cardiorespiratory Interaction Y1 - 1998 ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Hwang, Dong-Uk A1 - Chavez, Mario A1 - Amann, Andreas A1 - Kurths, Jürgen A1 - Pecora, Louis M. T1 - Synchronization in dynamical networks : evolution along commutative graphs N2 - Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.74.016102 SN - 1539-3755 ER - TY - JOUR A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Synchronization approach to analysis of biological systems N2 - In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach Y1 - 2004 SN - 0219-4775 ER - TY - JOUR A1 - Kurths, Jürgen A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Osipov, Grigory V. A1 - Ivanchenko, Mikhail V. A1 - Kiss, Istvan Z. A1 - Hudson, John L. T1 - Synchronization analysis of coupled noncoherent oscillators N2 - We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators Y1 - 2006 UR - http://www.springerlink.com/content/102972 U6 - https://doi.org/10.1007/s11071-006-1957-x SN - 0924-090X ER - TY - BOOK A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael A1 - Kurths, Jürgen T1 - Synchronization : a universal concept in nonlinear sciences T3 - Cambridge nonlinear science series Y1 - 2001 SN - 0-521-59285-2 VL - 12 PB - Cambridge Univ. Press CY - Cambridge ET - 1st paperback ed., repr ER - TY - JOUR A1 - Schiek, Michael A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Kurths, Jürgen A1 - Krampe, Ralf-Thomas A1 - Kliegl, Reinhold A1 - Drepper, Friedhelm R. T1 - Symbolic dynamics of physiological synchronisation : examples from bimanual movements and cardiorespiratory interaction N2 - Key words: Nonlinear time series analysis, symbolic dynamics, phase transitions, physiological data, biological synchronization, production of polyrhythms, cardiorespiratory interaction, variation of control parameter Y1 - 1997 ER - TY - JOUR A1 - Engbert, Ralf A1 - Scheffczyk, Christian A1 - Krampe, Ralf-Thomas A1 - Kurths, Jürgen A1 - Kliegl, Reinhold T1 - Symbolic dynamics of bimanual production of polyrhythms N2 - We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system. Y1 - 2002 SN - 3-540- 63481-9 ER - TY - JOUR A1 - Wessel, Niels A1 - Schwarz, Udo A1 - Saparin, Peter A1 - Kurths, Jürgen T1 - Symbolic dynamics for medical data analysis N2 - Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone. Y1 - 2002 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/EUROATTRACTOR2000.ps SN - 3-936142-09-2 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Symbolic dynamics behind the singular continuous power spectra of continuous flows Y1 - 1998 ER - TY - JOUR A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Timmer, Jens T1 - Surrogate-based hypothesis test without surrogates N2 - Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1 Y1 - 2004 SN - 0218-1274 ER - TY - JOUR A1 - Anishchenko, Vadim S. A1 - Kopeikin, A. S. A1 - Kurths, Jürgen T1 - Studying hyperbolicity in chaotic systems Y1 - 2000 ER - TY - JOUR A1 - Zemanova, Lucia A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Structural and functional clusters of complex brain networks JF - Physica, D, Nonlinear phenomena N2 - Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex. KW - cortical network KW - anatomical connectivity KW - functional connectivity KW - topological community KW - dynamical cluster Y1 - 2006 U6 - https://doi.org/10.1016/j.physd.2006.09.008 SN - 0167-2789 SN - 1872-8022 VL - 224 IS - 1-2 SP - 202 EP - 212 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Volkov, E. I. A1 - Ullner, Ekkehard A1 - Kurths, Jürgen T1 - Stochastic multiresonance in the coupled relaxation oscillators N2 - We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh- Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency. (C) 2005 American Institute of Physics Y1 - 2005 SN - 1054-1500 ER - TY - JOUR A1 - Zakharova, Anna A1 - Vadivasova, Tatjana A1 - Anishchenko, Vadim S. A1 - Koseska, Aneta A1 - Kurths, Jürgen T1 - Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator N2 - We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs. Y1 - 2010 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.81.011106 SN - 1539-3755 ER - TY - JOUR A1 - Kuznetsov, A. S. A1 - Kurths, Jürgen T1 - Stable heteroclinic cycles for ensembles of chaotic oscillators Y1 - 2002 ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen T1 - Spurious structures in recurrence plots induced by embedding N2 - In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay Y1 - 2006 U6 - https://doi.org/10.1007/s11071-006-2010-9 ER - TY - JOUR A1 - Anishchenko, Vadim S. A1 - Vadivasova, T. E. A1 - Kopeikin, A. S. A1 - Strelkova, G. I. A1 - Kurths, Jürgen T1 - Spectral and correlation analysis of spiral chaos N2 - We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when tau < tau(cor), and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. it is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp(-lambda(+)k), where lambda(+) is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator Y1 - 2003 SN - 0219-4775 ER - TY - JOUR A1 - Sun, Xiaojuan A1 - Lu, Qishao A1 - Kurths, Jürgen A1 - Wang, Qingyun T1 - Spatiotemporal coherence resonance in a map lattice N2 - We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively. Y1 - 2009 UR - http://www.worldscinet.com/ijbc/ijbc.shtml U6 - https://doi.org/10.1142/S021812740902310X SN - 0218-1274 ER - TY - JOUR A1 - Vasconcelos, D. B. A1 - Lopes, S. R. A1 - Viana, R. L. A1 - Kurths, Jürgen T1 - Spatial recurrence plots N2 - We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes Y1 - 2006 UR - http://pre.aps.org/pdf/PRE/v73/i5/e056207 U6 - https://doi.org/10.1103/Physreve.73.056207 ER - TY - JOUR A1 - Feudel, Ulrike A1 - Jansen, Wolfgang A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Voss, Henning U. T1 - Solar variability : simple models and proxy data Y1 - 1997 SN - 4-274-90187-4 ER - TY - INPR A1 - Pikovskij, Arkadij A1 - Zaks, Michael A. A1 - Feudel, Ulrike A1 - Kurths, Jürgen T1 - Singular continuous spectra in dissipative dynamics N2 - We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique. T3 - NLD Preprints - 15 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787 ER - TY - JOUR A1 - Schmidt, G. A1 - Zamora-Lopez, Gorka A1 - Kurths, Jürgen T1 - Simulation of large scale cortical networks by individual neuron dynamics N2 - Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required. Y1 - 2010 U6 - https://doi.org/10.1142/S0218127410026149 SN - 0218-1274 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Murali, K. A1 - Kurths, Jürgen T1 - Simple electronic circuit model for doubly stochastic resonance N2 - We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance. Y1 - 2001 UR - http://link.aps.org/abstract/PRE/v63/e020103 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes Y1 - 1999 ER - TY - JOUR A1 - Zou, Yong A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Bi, Q. T1 - Shrimp structure and associated dynamics in parametrically excited oscillators JF - International journal of bifurcation and chaos : in applied sciences and engineering N2 - We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system. KW - bifurcation analysis KW - recurrence plot KW - period doubling KW - intermittency Y1 - 2006 U6 - https://doi.org/10.1142/S0218127406016987 SN - 0218-1274 VL - 16 IS - 12 SP - 3567 EP - 3579 PB - World Scientific Publ. Co CY - Singapore ER - TY - JOUR A1 - Wessel, Niels A1 - Ziehmann, Christine A1 - Kurths, Jürgen A1 - Meyerfeldt, Udo A1 - Schirdewan, Alexander A1 - Voss, Andreas T1 - Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates N2 - Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF. Y1 - 2000 ER - TY - JOUR A1 - Winterhalder, Matthias A1 - Schelter, B A1 - Kurths, Jürgen A1 - Schulze-Borthage, A A1 - Timmer, Jens T1 - Sensitivity and specificity of coherence and phase synchronization analysis N2 - In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved Y1 - 2006 UR - http://www.sciencedirect.com/science/article/pii/S0375960106004002 ( 11.07.2011] U6 - https://doi.org/10.1016/j.physleta.2006.03.018 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks Y1 - 1999 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Self-organization of spatio-temporal earthquake clusters Y1 - 2000 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen A1 - Zschau, Jochen T1 - Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality Y1 - 2000 ER - TY - INPR A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij A1 - Scheffczyk, Christian T1 - Roughening interfaces in deterministic dynamics N2 - Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface. T3 - NLD Preprints - 3 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13447 ER - TY - JOUR A1 - Landa, Polina S. A1 - Ushakov, Vladimir A1 - Kurths, Jürgen T1 - Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals JF - Chaos, solitons & fractals : applications in science and engineering N2 - The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/09600779 U6 - https://doi.org/10.1016/j.chaos.2005.08.116 SN - 0960-0779 VL - 30 IS - 3 SP - 574 EP - 578 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Resonant patterns in noisy active media N2 - We investigate noise-controlled resonant response of active media to weak periodic forcing, both in excitable and oscillatory regimes. In the excitable regime, we find that noise-induced irregular wave structures can be reorganized into frequency-locked resonant patterns by weak signals with suitable frequencies. The resonance occurs due to a matching condition between the signal frequency and the noise-induced inherent time scale of the media. m:1 resonant regions similar to the Arnold tongues in frequency locking of self-sustained oscillatory media are observed. In the self-sustained oscillatory regime, noise also controls the oscillation frequency and reshapes significantly the Arnold tongues. The combination of noise and weak signal thus could provide an efficient tool to manipulate active extended systems in experiments Y1 - 2004 SN - 1063-651X ER - TY - JOUR A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Spahn, Frank A1 - Petzschmann, Olaf T1 - Reply on the comment of "Clustering of granular assemblies with temperature dependent restitution and under differential rotation" Y1 - 1998 ER - TY - JOUR A1 - Bergner, Andre A1 - Frasca, M. A1 - Sciuto, G. A1 - Buscarino, A. A1 - Ngamga, Eulalie Joelle A1 - Fortuna, L. A1 - Kurths, Jürgen T1 - Remote synchronization in star networks JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.026208 SN - 1539-3755 VL - 85 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Osipov, Grigory V. A1 - Kurths, Jürgen T1 - Regular and chaotic phase synchronization of coupled circle maps Y1 - 2002 ER - TY - JOUR A1 - Marwan, Norbert A1 - Wessel, Niels A1 - Meyerfeldt, Udo A1 - Schirdewan, Alexander A1 - Kurths, Jürgen T1 - Recurrence-plot-based measures of complexity and its application to heart-rate-variability data N2 - The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias. Y1 - 2002 UR - http://arxiv.org/abs/physics/0201064 ER - TY - JOUR A1 - Wessel, Niels A1 - Marwan, Norbert A1 - Meyerfeldt, Udo A1 - Schirdewan, Alexander A1 - Kurths, Jürgen T1 - Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia N2 - Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the Y1 - 2001 UR - http://link.springer.de/link/service/series/0558/bibs/2199/21990295.htm ER - TY - JOUR A1 - Marwan, Norbert A1 - Schinkel, Stefan A1 - Kurths, Jürgen T1 - Recurrence plots 25 years later -Gaining confidence in dynamical transitions JF - epl : a letters journal exploring the frontiers of physics N2 - Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots. Y1 - 2013 U6 - https://doi.org/10.1209/0295-5075/101/20007 SN - 0295-5075 VL - 101 IS - 2 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Ramos, Antonio M. T. A1 - Builes-Jaramillo, Alejandro A1 - Poveda, German A1 - Goswami, Bedartha A1 - Macau, Elbert E. N. A1 - Kurths, Jürgen A1 - Marwan, Norbert T1 - Recurrence measure of conditional dependence and applications JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevE.95.052206 SN - 2470-0045 SN - 2470-0053 VL - 95 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Voss, Henning U. A1 - Kurths, Jürgen T1 - Reconstruction of nonlinear time-delayed feedback models from optical data Y1 - 1999 ER - TY - JOUR A1 - Voss, Henning U. A1 - Kurths, Jürgen T1 - Reconstruction of nonlinear time delay models from data by the use of optimal transformations Y1 - 1997 ER - TY - INPR A1 - Voss, Henning A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis N2 - Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record. T3 - NLD Preprints - 28 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14083 ER - TY - JOUR A1 - Petrov, Valko A1 - Kurths, Jürgen A1 - Georgiev, Nikola T1 - Reconstructing differential equation from a time series N2 - This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient Y1 - 2003 SN - 0218-1274 ER - TY - JOUR A1 - Rusconi, Marco A1 - Valleriani, Angelo A1 - Dunlop, John William Chapman A1 - Kurths, Jürgen A1 - Weinkamer, Richard T1 - Quantitative approach to the stochastics of bone remodeling JF - epl : a letters journal exploring the frontiers of physics N2 - During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age. Y1 - 2012 U6 - https://doi.org/10.1209/0295-5075/97/28009 SN - 0295-5075 VL - 97 IS - 2 PB - EDP Sciences CY - Mulhouse ER - TY - INPR A1 - Kurths, Jürgen A1 - Voss, A. A1 - Witt, Annette A1 - Saparin, P. A1 - Kleiner, H. J. A1 - Wessel, Niels T1 - Quantitative analysis of heart rate variability N2 - In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. T3 - NLD Preprints - 5 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13470 ER - TY - JOUR A1 - Shabunin, A. A1 - Astakhov, Vladimir V. A1 - Kurths, Jürgen T1 - Quantitative analysis of chaotic synchronization by means of coherence N2 - We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Marwan, Norbert A1 - Beller, Gise A1 - Felsenberg, Dieter A1 - Saparin, Peter A1 - Kurths, Jürgen T1 - quantifying changes in the spatial structure of trabecular bone JF - International journal of bifurcation and chaos : in applied sciences and engineering N2 - We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization. KW - 3D medical image analysis KW - pQCT KW - trabecular bone KW - patient immobilization Y1 - 2012 U6 - https://doi.org/10.1142/S0218127412500277 SN - 0218-1274 VL - 22 IS - 2 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Saparin, P. I. A1 - Thomsen, J. S. A1 - Prohaska, Steffen A1 - Zaikin, Alexei A1 - Kurths, Jürgen A1 - Hege, H. C. A1 - Gowin, W. T1 - Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity N2 - Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved Y1 - 2005 SN - 0094-5765 ER - TY - JOUR A1 - Tokuda, I. A1 - Kurths, Jürgen A1 - Allaria, Eugenio A1 - Meucci, Riccardo A1 - Boccaletti, Stefano A1 - Arecchi, Fortunato Tito T1 - Predicting phase synchronization in a spiking chaotic CO2 laser N2 - An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments Y1 - 2004 SN - 1063-651X ER - TY - INPR A1 - Guasti, Giovanna A1 - Engbert, Ralf A1 - Krampe, Ralf T. A1 - Kurths, Jürgen T1 - Phase transitions, complexity, and stationarity in the production of polyrhythms N2 - Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook T3 - NLD Preprints - 57 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14933 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael A1 - Zaks, Michael A. A1 - Kurths, Jürgen T1 - Phase synchronization of regular and chaotic oscillators Y1 - 1999 ER - TY - JOUR A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Phase Synchronization of Chaotic Rotators N2 - We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor. Y1 - 2002 ER - TY - JOUR A1 - Rosenblum, Michael A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Phase synchronization of chaotic oscillators by external driving Y1 - 1997 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Osipov, Grigory V. A1 - Kurths, Jürgen T1 - Phase synchronization of chaotic oscillations in terms of periodic orbits Y1 - 1997 SN - 1054-1500 ER - TY - JOUR A1 - Ivanchenko, Mikhail V. A1 - Osipov, Grigory V. A1 - Shalfeev, V. D. A1 - Kurths, Jürgen T1 - Phase synchronization of chaotic intermittent oscillations N2 - We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization Y1 - 2004 SN - 0031-9007 ER - TY - JOUR A1 - Park, Eun Hyoung A1 - Zaks, Michael A. A1 - Kurths, Jürgen T1 - Phase synchronization in the forced lorenz system Y1 - 1999 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael A1 - Kurths, Jürgen T1 - Phase synchronization in regular and chaotic systems Y1 - 2000 SN - 0218-1274 ER - TY - JOUR A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Phase synchronization in noisy and chaotic oscillators Y1 - 1997 ER - TY - JOUR A1 - Ivanchenko, Mikhail V. A1 - Osipov, Grigory V. A1 - Shalfeev, V. D. A1 - Kurths, Jürgen T1 - Phase synchronization in ensembles of bursting oscillators N2 - We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles Y1 - 2004 SN - 0031-9007 ER -