TY - JOUR A1 - Gowin, W. A1 - Saparin, Peter A1 - Kurths, Jürgen A1 - Felsenberg, D. T1 - Bone Architecture assessment with Measures of Complexity Y1 - 2001 ER - TY - JOUR A1 - Gowin, W. A1 - Saparin, Peter A1 - Kurths, Jürgen T1 - Bone architecture quantification: Measures of complexity compared to failure lead results Y1 - 2001 ER - TY - JOUR A1 - Anishchenko, Vadim S. A1 - Vadivasova, T. E. A1 - Kopeikin, A. S. A1 - Kurths, Jürgen A1 - Strelkova, G. I. T1 - Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors Y1 - 2001 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 - 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 and noise-induced nonequilibrium phase transitions Y1 - 2000 SN - 1-563-96826-6 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 - Landa, Polina S. A1 - Zaikin, Alexei A. A1 - Ushakov, V. G. A1 - Kurths, Jürgen T1 - Influence of additive noise on transitions in nonlinear systems N2 - The effect of additive noise on transitions in nonlinear systems far from equilibrium is studied. It is shown that additive noise in itself can induce a hidden phase transition, which is similar to the transition induced by multiplicative noise in a nonlinear oscillator [P. Landa and A. Zaikin, Phys. Rev. E 54, 3535 (1996)]. Investigation of different nonlinear models that demonstrate phase transitions induced by multiplicative noise shows that the influence of additive noise upon such phase transitions can be crucial: additive noise can either blur such a transition or stabilize noise-induced oscillations. Y1 - 2000 UR - http://link.aps.org/abstract/PRE/v61/p4809 ER - TY - JOUR A1 - Landa, Polina S. A1 - Zaikin, Alexei A A1 - Kurths, Jürgen T1 - On noise-induced transitions in nonlinear oscillators Y1 - 2000 SN - 3-540- 41074-0 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 - 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 - 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 - JOUR A1 - Anishchenko, Vadim S. A1 - Kopeikin, A. S. A1 - Kurths, Jürgen T1 - Studying hyperbolicity in chaotic systems Y1 - 2000 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 - Boccaletti, Stefano A1 - Valladares, D. L. A1 - Kurths, Jürgen T1 - Synchronization of chaotic structurally nonequivalent systems Y1 - 2000 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 - 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 - 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 - Lai, Ying Cheng A1 - Grebogi, Celso A1 - Kurths, Jürgen T1 - Modeling of deterministic chaotic systems Y1 - 1999 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 - 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 - Voss, Henning U. A1 - Kurths, Jürgen T1 - Reconstruction of nonlinear time-delayed feedback models from optical data Y1 - 1999 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 - Zaikin, Alexei A. A1 - Kurths, Jürgen T1 - Modeling Cognitive Control in Simple Movements Y1 - 1999 SN - 1-563-96863-0 ER - TY - JOUR A1 - Kolodner, P. A1 - Abel, Markus A1 - Kurths, Jürgen A1 - Voss, Henning U. T1 - Amplitude equations from spatiotemporal binary-fluid convection data Y1 - 1999 UR - http://www.stat.physik.uni-potsdam.de/~markus/papers/PRL83-3422.pdf 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 - 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 - 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 - Park, Eun Hyoung A1 - Rosenblum, Michael A1 - Kurths, Jürgen A1 - Zaks, Michael A. T1 - Alternating locking ratios in imperfect phase synchronization Y1 - 1999 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 - 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 - GEN A1 - Motter, Adilson E. A1 - Matias, Manuel A. A1 - Kurths, Jürgen A1 - Ott, Edward T1 - Dynamics on complex networks and applications T2 - Physica. D, Nonlinear phenomena KW - complex systems KW - nonlinear dynamics KW - statistical physics Y1 - 2006 U6 - https://doi.org/10.1016/j.physd.2006.09.012 SN - 0167-2789 VL - 224 IS - 1-2 SP - VII EP - VIII PB - Elsevier CY - Amsterdam 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 - 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 - 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 - 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 - Kurths, Jürgen A1 - Pikovskij, Arkadij T1 - Comment on "Phase synchronization in discrete chaotic systems" N2 - Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful. 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 - Pikovskij, Arkadij A1 - Rosenblum, Michael A1 - Kurths, Jürgen T1 - Phase synchronization in regular and chaotic systems Y1 - 2000 SN - 0218-1274 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 - 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 - 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 - 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 - 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 - 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 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Coherence Resonance in a Noise-Driven Excitable System N2 - We study the dynamics of the excitable Fitz Hugh-Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon. Y1 - 1997 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 - 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 - 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 - Witt, Annette A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij T1 - Testing stationarity in time series Y1 - 1998 ER -