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 - Boccaletti, Stefano A1 - Hwang, Dong-Uk A1 - Chavez, Mario A1 - Amann, Andreas A1 - Kurths, Jürgen A1 - Pecora, Louis M. T1 - Synchronization in dynamical networks : evolution along commutative graphs N2 - Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.74.016102 SN - 1539-3755 ER - TY - JOUR A1 - Rosenblum, Michael A1 - 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 - 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 - Huang, Tingwen A1 - Chen, Guanrong A1 - Kurths, Jürgen T1 - Synchronization of chaotic of chaotic systems with time-varying coupöing delays JF - Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations N2 - In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation in equalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method. KW - Synchronization KW - Chaotic System KW - Time-varying Delay Y1 - 2011 U6 - https://doi.org/10.3934/dcdsb.2011.16.1071 SN - 1531-3492 VL - 16 IS - 4 SP - 1071 EP - 1082 PB - American Institute of Mathematical Sciences CY - Springfield ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Valladares, D. L. A1 - Kurths, Jürgen T1 - Synchronization of chaotic structurally nonequivalent systems Y1 - 2000 ER - TY - JOUR A1 - Li, Changpin A1 - Sun, Weigang A1 - Kurths, Jürgen T1 - Synchronization of complex dynamical networks with time delays N2 - In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/03784371 U6 - https://doi.org/10.1016/j.physa.2005.07.007 SN - 0378-4371 ER - TY - JOUR A1 - Meucci, Riccardo A1 - Salvadori, Francesco A1 - Ivanchenko, Mikhail V. A1 - Al Naimee, Kais A1 - Zhou, Chansong A1 - Arecchi, Fortunato Tito A1 - Boccaletti, Stefano A1 - Kurths, Jürgen T1 - Synchronization of spontaneous bursting in a CO2 laser JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling. Y1 - 2006 U6 - https://doi.org/10.1103/PhysRevE.74.066207 SN - 2470-0045 SN - 2470-0053 VL - 74 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Montbrio, Ernest A1 - Kurths, Jürgen A1 - Blasius, Bernd T1 - Synchronization of two interacting populations of oscillators N2 - We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/pre3.pdf ER - TY - JOUR A1 - Ivanchenko, Mikhail V. A1 - Osipov, Grigory V. A1 - Shalfeev, V. D. A1 - Kurths, Jürgen T1 - Synchronization of two non-scalar-coupled limit-cycle oscillators N2 - Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved Y1 - 2004 ER - TY - JOUR A1 - Srinivasan, K. A1 - Senthilkumar, Dharmapuri Vijayan A1 - Murali, K. A1 - Lakshmanan, Muthusamy A1 - Kurths, Jürgen T1 - Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay tau(1) and coupling delay tau(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay tau(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems. Y1 - 2011 U6 - https://doi.org/10.1063/1.3591791 SN - 1054-1500 VL - 21 IS - 2 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Osipov, Grigory V. A1 - Ivanchenko, Mikhail V. A1 - Kurths, Jürgen A1 - Hu, B. T1 - Synchronized chaotic intermittent and spiking behavior in coupled map chains N2 - We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Kitajima, H. A1 - Kurths, Jürgen T1 - Synchronized firing of FitzHugh-Nagumo neurons by noise N2 - We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. (C) 2005 American Institute of Physics Y1 - 2005 SN - 1054-1500 ER - TY - JOUR A1 - Koseska, Aneta A1 - Volkov, Evgenii A1 - Kurths, Jürgen T1 - Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits JF - Physica scripta : an international journal for experimental and theoretical physics N2 - Synthetic biology is a relatively new research discipline that combines standard biology approaches with the constructive nature of engineering. Thus, recent efforts in the field of synthetic biology have given a perspective to consider cells as 'programmable matter'. Here, we address the possibility of using synthetic circuits to control protein dynamics. In particular, we show how intercellular communication and stochasticity can be used to manipulate the dynamical behavior of a population of coupled synthetic units and, in this manner, finely tune the expression of specific proteins of interest, e.g. in large bioreactors. Y1 - 2011 U6 - https://doi.org/10.1088/0031-8949/84/04/045007 SN - 0031-8949 VL - 84 IS - 4 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - 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 - Voss, Henning U. A1 - Kurths, Jürgen T1 - Test for nonlinear dynamical behavior in symbol sequences Y1 - 1998 ER - TY - JOUR A1 - Riedl, Maik A1 - van Leeuwen, Peter Jan A1 - Suhrbier, Alexander A1 - Malberg, Hagen A1 - Groenemeyer, Dietrich A1 - Kurths, Jürgen A1 - Wessel, Niels T1 - Testing foetal-maternal heart rate synchronization via model-based analyses N2 - The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization. Y1 - 2009 UR - http://rsta.royalsocietypublishing.org/ U6 - https://doi.org/10.1098/rsta.2008.0277 SN - 1364-503X ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Parlitz, Ulrich A1 - Sonett, Charles P. T1 - Testing for nonlinearity in radiocarbon data N2 - The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum. Y1 - 1994 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/n.ps.gz SN - 1023-5809 ER - TY - JOUR A1 - Allefeld, Carsten A1 - Kurths, Jürgen T1 - Testing for phase synchronization N2 - We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series Y1 - 2004 SN - 0218-1274 ER - TY - JOUR A1 - Engbert, Ralf A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Testing for unstable periodic orbits to characterize spatiotemporal dynamics Y1 - 1998 ER -