TY - JOUR A1 - Zöller, Gert A1 - Hainzl, Sebastian A1 - Kurths, Jürgen T1 - Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes Y1 - 2001 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 - Ziehmann, Christine A1 - Smith, Leonard A. A1 - Kurths, Jürgen T1 - Localized Lyapunov exponents and the prediction of predictability Y1 - 2000 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 - Zhou, Changsong A1 - Zemanova, Lucia A1 - Zamora, Gorka A1 - Hilgetag, Claus C. A1 - Kurths, Jürgen T1 - Hierarchical organization unveiled by functional connectivity in complex brain networks JF - Physical review letters N2 - How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks. Y1 - 2006 U6 - https://doi.org/10.1103/PhysRevLett.97.238103 SN - 0031-9007 SN - 1079-7114 VL - 97 PB - American Physical Society CY - College Park 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 - JOUR A1 - Zhou, Changsong A1 - Kurths, Jürgen A1 - Kiss, Istvan Z. A1 - Hudson, J. L. T1 - Noise-enhanced phase synchronization of chaotic oscillators Y1 - 2002 ER - TY - JOUR A1 - Zhou, Changsong A1 - Kurths, Jürgen A1 - Hu, B. T1 - Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise Y1 - 2001 ER - TY - JOUR A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Noise-sustained and controlled synchronization of stirred excitable media by external forcing N2 - Most of the previous studies on constructive effects of noise in spatially extended systems have focused on static media, e.g., of the reaction diffusion type. Because many active chemical or biological processes occur in a fluid environment with mixing, we investigate here the interplay among noise, excitability, mixing and external forcing in excitable media advected by a chaotic flow, in a two-dimensional FitzHugh-Nagumo model described by a set of reaction- advection-diffusion equations. In the absence of external forcing, noise may generate sustained coherent oscillations of the media in a range of noise intensities and stirring rates. We find that these noise-sustained oscillations can be synchronized by external periodic signals much smaller than the threshold. Analysis of the locking regions in the parameter space of the signal period, stirring rate and noise intensity reveals that the mechanism underlying the synchronization behaviour is a matching between the time scales of the forcing signal and the noise-sustained oscillations. The results demonstrate that, in the presence of a suitable level of noise, the stirred excitable media act as self-sustained oscillatory systems and become much easier to be entrained by weak external forcing. Our results may be verified in experiments and are useful to understand the synchronization of population dynamics of oceanic ecological systems by annual cycles Y1 - 2005 SN - 1367-2630 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 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Dynamical weights and enhanced synchronization in adaptive complex networks N2 - Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks Y1 - 2006 UR - http://link.aps.org/doi/10.1103/PhysRevLett.96.164102 U6 - https://doi.org/10.1103/Physrevlett.96.164102 ER - TY - JOUR A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Hierarchical synchronization in complex networks with heterogeneous degrees N2 - We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics Y1 - 2006 UR - http://scitation.aip.org/getpdf/servlet/ GetPDFServlet?filetype=pdf&id=CHAOEH000016000001015104000001&idtype=cvips&doi=10.1063/1.2150381&prog=normal U6 - https://doi.org/10.1063/1.2150381 SN - 1054-1500 ER - TY - JOUR A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Noise-induced phase synchronization and synchronization transitions in chaotic oscillators Y1 - 2002 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 - 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 - 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 - Zaks, Michael A. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - On the generalized dimensions for the fourier spectrum of the thue-morse sequence Y1 - 1999 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 - Zaks, Michael A. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - On the correlation dimension of the spectral measure for the Thue-Morse sequence Y1 - 1997 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Park, Eun Hyoung A1 - Kurths, Jürgen T1 - On phase synchronization by periodic force in chaotic oscillators with saddle equilibria Y1 - 2000 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 - Zakharova, Anna A1 - Kurths, Jürgen A1 - Vadivasova, Tatyana A1 - Koseska, Aneta T1 - Analysing dynamical behavior of cellular networks via stochastic bifurcations JF - PLoS one N2 - The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types. Y1 - 2011 U6 - https://doi.org/10.1371/journal.pone.0019696 SN - 1932-6203 VL - 6 IS - 5 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Zaikin, Alexey A1 - Kurths, Jürgen T1 - Optimal length transportation hypothesis to model proteasome product size distribution JF - Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences N2 - This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport. KW - proteasome KW - protein translocation KW - stochastic process KW - ratchets Y1 - 2006 U6 - https://doi.org/10.1007/s10867-006-9014-z SN - 0092-0606 VL - 32 IS - 3-4 SP - 231 EP - 243 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Zaikin, Alexei A1 - Kurths, Jürgen A1 - Saparin, Peter A1 - Gowin, W. A1 - Prohaska, Steffen T1 - Modeling bone resorption in 2D CT and 3D mu CT images N2 - We study several algorithms to simulate bone mass loss in two-dimensional and three-dimensional computed tomography bone images. The aim is to extrapolate and predict the bone loss, to provide test objects for newly developed structural measures, and to understand the physical mechanisms behind the bone alteration. Our bone model approach differs from those already reported in the literature by two features. First, we work with original bone images, obtained by computed tomography (CT); second, we use structural measures of complexity to evaluate bone resorption and to compare it with the data provided by CT. This gives us the possibility to test algorithms of bone resorption by comparing their results with experimentally found dependencies of structural measures of complexity, as well as to show efficiency of the complexity measures in the analysis of bone models. For two-dimensional images we suggest two algorithms, a threshold algorithm and a virtual slicing algorithm. The threshold algorithm simulates bone resorption on a boundary between bone and marrow, representing an activity of osteoclasts. The virtual slicing algorithm uses a distribution of the bone material between several virtually created slices to achieve statistically correct results, when the bone-marrow transition is not clearly defined. These algorithms have been tested for original CT 10 mm thick vertebral slices and for simulated 10 mm thick slices constructed from ten I mm thick slices. For three-dimensional data, we suggest a variation of the threshold algorithm and apply it to bone images. The results of modeling have been compared with CT images using structural measures of complexity in two- and three-dimensions. This comparison has confirmed credibility of a virtual slicing modeling algorithm for two-dimensional data and a threshold algorithm for three-dimensional data Y1 - 2005 SN - 0218-1274 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Rosenblum, Michael A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Krampe, Ralf-Thomas A1 - Kurths, Jürgen T1 - Modeling qualitative changes in bimanual movements Y1 - 1997 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Rosenblum, Michael A1 - Landa, Polina S. A1 - Kurths, Jürgen T1 - On-off itermittency phenomena in a pendulum with a randomly vibrating suspension axis Y1 - 1998 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Rosenblum, Michael A1 - Landa, Polina S. A1 - Kurths, Jürgen T1 - Control of noise-induced oscillations of a pendulum with a rondomly vibrating suspension axis Y1 - 1997 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 - 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 - Zaikin, Alexei A. A1 - Kurths, Jürgen A1 - Schimansky-Geier, Lutz T1 - Doubly stochastic resonance N2 - We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement. Y1 - 2000 UR - http://link.aps.org/abstract/PRL/v85/p227 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Kurths, Jürgen T1 - Additive noise in noise-induced nonequilibrium transitions Y1 - 2001 SN - 1054-1500 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Kurths, Jürgen T1 - Additive noise and noise-induced nonequilibrium phase transitions Y1 - 2000 SN - 1-563-96826-6 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - Kurths, Jürgen T1 - Modeling Cognitive Control in Simple Movements Y1 - 1999 SN - 1-563-96863-0 ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - García-Ojalvo, Jordi A1 - Schimansky-Geier, Lutz A1 - Kurths, Jürgen T1 - Noise induced propagation in monostable media N2 - We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium i observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits. Y1 - 2002 UR - http://link.aps.org/abstract/PRL/v88/e010601 ER - TY - JOUR A1 - Wu, Ye A1 - Zhou, Changsong A1 - Chen, Maoyin A1 - Xiao, Jinghua A1 - Kurths, Jürgen T1 - Human comment dynamics in on-line social systems N2 - Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society. Y1 - 2010 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2010.08.049 SN - 0378-4371 ER - TY - JOUR A1 - Wu, Ye Wu A1 - Zhou, Changsong A1 - Xiao, Jinghua A1 - Kurths, Jürgen A1 - Schellnhuber, Hans Joachim T1 - Evidence for a bimodal distribution in human communication N2 - Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc. Y1 - 2010 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1073/pnas.1013140107 SN - 0027-8424 ER - TY - INPR A1 - Witt, Annette A1 - Neiman, Alexander A1 - Kurths, Jürgen T1 - Characterizing the dynamics of stochastic bistable systems by measures of complexity N2 - 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. T3 - NLD Preprints - 36 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14556 ER - TY - BOOK A1 - Witt, Annette A1 - Neiman, Alexander A1 - Kurths, Jürgen T1 - Characterizing the dynamics of stochastic bistable systems by measures of complexity T3 - Preprint NLD Y1 - 1997 SN - 1432-2935 VL - 36 PB - Univ. Potsdam CY - Potsdam ER - TY - JOUR A1 - Witt, Annette A1 - Neiman, Alexander A1 - Kurths, Jürgen T1 - Charakterizing the dynamics of stochastic bistable systems by measures of complexity Y1 - 1997 ER - TY - JOUR A1 - Witt, Annette A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij T1 - Testing stationarity in time series Y1 - 1998 ER - TY - INPR A1 - Witt, Annette A1 - Kurths, Jürgen A1 - Krause, F. A1 - Fischer, K. T1 - On the validity of a model for the reversals of the Earth‘s magnetic field N2 - We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information. T3 - NLD Preprints - 4 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13460 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 - 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 - Wessel, Niels A1 - Voss, Andreas A1 - Malberg, Hagen A1 - Ziehmann, Christine A1 - Voss, Henning U. A1 - Schirdewan, Alexander A1 - Meyerfeldt, Udo A1 - Kurths, Jürgen T1 - Nonlinear analysis of complex phenomena in cardiological data N2 - The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators. Y1 - 2000 ER - TY - JOUR A1 - Wessel, Niels A1 - Voss, Andreas A1 - Kurths, Jürgen A1 - Schirdewan, Alexander A1 - Hnatkova, Katarina A1 - Malik, Marek T1 - Evaluation of renormalised entropy for risk stratification using heart rate variability data N2 - Standard time and frequency parameters of heart rate variability (HRV) describe only linear and periodic behaviour, whereas more complex relationships cannot be recognised. A method that may be capable of assessing more complex properties is the non-linear measure of 'renormalised entropy.' A new concept of the method, RE(AR), has been developed, based on a non-linear renormalisation of autoregressive spectral distributions. To test the hypothesis that renormalised entropy may improve the result of high-risk stratification after myocardial infarction, it is applied to a clinical pilot study (41 subjects) and to prospective data of the St George's Hospital post- infarction database (572 patients). The study shows that the new RE(AR) method is more reproducible and more stable in time than a previously introduced method (p<0.001). Moreover, the results of the study confirm the hypothesis that on average, the survivors have negative values of RE(AR) (-0.11+/-0.18), whereas the non-survivors have positive values (0.03+/-0.22, p<0.01). Further, the study shows that the combination of an HRV triangular index and RE(AR) leads to a better prediction of sudden arrhythmic death than standard measurements of HRV. In summary, the new RE(AR) method is an independent measure in HRV analysis that may be suitable for risk stratification in patients after myocardial infarction. Y1 - 2000 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 - Wessel, Niels A1 - Schumann, Agnes A1 - Wessel, Niels A1 - Schumann, Agnes A1 - Schirdewan, Alexander A1 - Voss, Andreas A1 - Kurths, Jürgen T1 - Entropy measures in heart rate variability data Y1 - 2000 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 - Wessel, Niels A1 - Kleiner, H. J. A1 - Voss, Andreas A1 - Kurths, Jürgen A1 - Dietz, R. T1 - Nonlinear dynamics in cardiovasscular diseases Y1 - 1997 ER - TY - JOUR A1 - Voss, Henning U. A1 - Timmer, Jens A1 - Kurths, Jürgen T1 - Nonlinear dynamical system identification from uncertain and indirect measurements N2 - We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples Y1 - 2004 SN - 0218-1274 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 - 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 - JOUR A1 - Voss, Henning U. A1 - Kurths, Jürgen T1 - Reconstruction of nonlinear time-delayed feedback models from optical data Y1 - 1999 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 - Volkov, E. I. A1 - Ullner, Ekkehard A1 - Zaikin, Alexei A. A1 - Kurths, Jürgen T1 - Frequency-dependent stochastic resonance in inhibitory coupled excitable systems N2 - We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations Y1 - 2003 SN - 1063-651X 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 - 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 - Viana, R. L. A1 - Grebogi, Celso A1 - Pinto, S. E. D. A1 - Lopes, S. R. A1 - Batista, A. M. A1 - Kurths, Jürgen T1 - Bubbling bifurcation : loss of synchronization and shadowing breakdown in complex systems N2 - 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 Y1 - 2005 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 - Tokuda, I. A1 - Kurths, Jürgen A1 - Rosa, Epaminondas T1 - Learning phase synchronization from nonsynchronized chaotic regimes Y1 - 2002 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 - Thiessenhusen, Kai-Uwe A1 - Esposito, Larry W. A1 - Kurths, Jürgen A1 - Spahn, Frank T1 - Detection of hidden resonances in Saturn's B-ring N2 - The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances. T3 - NLD Preprints - 13 KW - Planetary Rings Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13618 ER - TY - GEN A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin A1 - Kliegl, Reinhold T1 - Generating Surrogates from Recurrences N2 - In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - paper 238 KW - Æ Recurrence Plots KW - Surrogate Data KW - Hypothesis Test KW - Phase Synchronization Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56906 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 - 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 - 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 - Thiel, M. A1 - Romano, Maria Carmen A1 - Read, P. L. A1 - Kurths, Jürgen T1 - Estimation of dynamical invariants without embedding by recurrence plots N2 - In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics Y1 - 2004 SN - 1054-1500 ER - TY - JOUR A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Kurths, Jürgen T1 - How much information is contained in a recurrence plot? N2 - Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved Y1 - 2004 SN - 0375-9601 ER - TY - JOUR A1 - Tass, Peter A1 - Rosenblum, Michael A1 - Weule, J. A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij A1 - Volkmann, J. A1 - Schnitzler, A. A1 - Freund, H.-J. T1 - Detection of n:m phase locking from noisy data : application to magnetoencephalography N2 - We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that Y1 - 1998 ER - TY - JOUR A1 - Surovyatkina, E. D. A1 - Kravtsov, Y. A. A1 - Kurths, Jürgen T1 - Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking N2 - We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Suresh, R. A1 - Senthilkumar, Dharmapuri Vijayan A1 - Lakshmanan, Muthusamy A1 - Kurths, Jürgen T1 - Global phase synchronization in an array of time-delay systems N2 - We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase. Y1 - 2010 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.82.016215 SN - 1539-3755 ER - TY - JOUR A1 - 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 - Stolbova, Veronika A1 - Surovyatkina, Elena A1 - Bookhagen, Bodo A1 - Kurths, Jürgen T1 - Tipping elements of the Indian monsoon: Prediction of onset and withdrawal JF - Geophysical research letters N2 - Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation. Y1 - 2016 U6 - https://doi.org/10.1002/2016GL068392 SN - 0094-8276 SN - 1944-8007 VL - 43 SP - 3982 EP - 3990 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Steuer, Ralf A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Constructive effects of fluctuations in genetic and biochemical regulatory systems N2 - Biochemical and genetic regulatory systems that involve low concentrations of molecules are inherently noisy. This intrinsic stochasticity, has received considerable interest recently, leading to new insights about the sources and consequences of noise in complex systems of genetic regulation. However, most prior work was devoted to the reduction of fluctuation and the robustness of cellular function with respect to intrinsic noise. Here, we focus on several scenarios in which the inherent molecular fluctuations are not merely a nuisance, but act constructively and bring about qualitative changes in the dynamics of the system. It will be demonstrated that in many typical situations biochemical and genetic regulatory systems may utilize intrinsic noise to their advantage. (C) 2002 Elsevier Ireland Ltd. All rights reserved Y1 - 2003 SN - 0303-2647 ER - TY - JOUR A1 - Steuer, Ralf A1 - Kurths, Jürgen A1 - Fiehn, Oliver A1 - Weckwerth, Wolfram T1 - Interpreting correlations in metabolomic networks N2 - Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. in this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways Y1 - 2003 SN - 0300-5127 ER - TY - JOUR A1 - Spahn, Frank A1 - Schwarz, Udo A1 - Kurths, Jürgen T1 - Clustering of granular assemblies with temperature dependent restitution under Keplerian differential rotation Y1 - 1997 ER - TY - JOUR A1 - Spahn, Frank A1 - Katzorke, Ines A1 - Petzschmann, Olaf A1 - Schwarz, Udo A1 - Kurths, Jürgen T1 - Cluster instabiliy of granular assemblies Y1 - 1997 ER - TY - JOUR A1 - Sitz, Andre A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Voss, Henning U. T1 - Estimation of parameters and unobserved components for nonlinear systems from noisy time series N2 - We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data. Y1 - 2002 UR - http://pre.aps.org/ 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 - Senthilkumar, Dharmapuri Vijayan A1 - Kurths, Jürgen T1 - Characteristics and synchronization of time-delay systems driven by a common noise N2 - We investigate the characteristics of time-delay systems in the presence of Gaussian noise. We show that the delay time embedded in the time series of time-delay system with constant delay cannot be estimated in the presence noise for appropriate values of noise intensity thereby forbidding any possibility of phase space reconstruction. We also demonstrate the existence of complete synchronization between two independent identical time-delay systems driven by a common noise without explicitly establishing any external coupling between them. Y1 - 2010 UR - http://www.springerlink.com/content/1951-6355 U6 - https://doi.org/10.1140/epjst/e2010-01273-4 SN - 1951-6355 ER - TY - JOUR A1 - Schwarz, Udo A1 - Spahn, Frank A1 - Grebogi, Celso A1 - Kurths, Jürgen A1 - Petzschmann, Olaf T1 - Length scales of clustering in granular gases Y1 - 1999 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 - Schwache, A. A1 - Kurths, Jürgen A1 - Mitschke, F. A1 - Voss, Henning U. T1 - Equations of motion from chaotic data : a driven optical fiber ring resonator Y1 - 1999 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 - 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 - Schelter, Björn A1 - Winterhalder, Matthias A1 - Dahlhaus, Rainer A1 - Kurths, Jürgen A1 - Timmer, Jens T1 - Partial phase synchronization for multivariate synchronizing systems N2 - Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated Y1 - 2006 UR - http://prl.aps.org/abstract/PRL/v96/i20/e208103 U6 - https://doi.org/10.1103/Physrevlett.96.208103 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 - JOUR A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Kurths, Jürgen A1 - Krampe, Ralf-Thomas A1 - Kliegl, Reinhold T1 - Nonlinear Phenomena in Polyrhythmic Hand Movements N2 - In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed. Y1 - 1995 SN - 981-02-2689-6 ER - TY - JOUR A1 - Scheffczyk, Christian A1 - Engbert, Ralf A1 - Krampe, Ralf-Thomas A1 - Kurths, Jürgen A1 - Rosenblum, Michael A1 - Zaikin, Alexei A. T1 - Nonlinear Modelling of Polyrhythmic Hand Movements Y1 - 1996 ER - TY - JOUR A1 - Saparin, Peter A1 - Kurths, Jürgen A1 - Gowin, P. A1 - Felsenberg, D. T1 - Die quantitative Beurteilung trabeculärer Knochenstrukturen der Lendenwirbelkörper durch Meßmethoden der nicht-linearen Dynamik Y1 - 1997 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 - Ruzick, Oliver A1 - Scheffczyk, Christian A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Dynamics of chaos-order interface in coupled map lattices Y1 - 1997 ER - TY - JOUR A1 - Rusconi, Marco A1 - Valleriani, Angelo A1 - Dunlop, John William Chapman A1 - Kurths, Jürgen A1 - Weinkamer, Richard T1 - Insights into the control of trabecular bone remodelling obtained by a Markov model Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/87563282 U6 - https://doi.org/10.1016/j.bone.2009.03.467 SN - 8756-3282 ER - TY - JOUR A1 - 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 - BOOK A1 - Rosenblum, Michael A1 - Schäfer, Carsten A1 - Abel, Hans-Henning A1 - Kurths, Jürgen T1 - Interrelationship of Parasympathetic Innervation of the Sinoatrial Node and the Atrioventricular Node of Human Heart Y1 - 1997 SN - 1120-1797 ER - TY - JOUR A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen A1 - Osipov, Grigory V. A1 - Kiss, Istvan Z. A1 - Hudson, J. L. T1 - Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics Y1 - 2002 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 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - From Phase to Lag Synchronization in Coupled Chaotic Oscillators N2 - We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum. Y1 - 1997 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 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Phase synchronization in driven and coupled chaotic oscillators Y1 - 1997 ER -