TY - JOUR A1 - Kurths, Jürgen A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Osipov, Grigory V. A1 - Ivanchenko, Mikhail V. A1 - Kiss, Istvan Z. A1 - Hudson, John L. T1 - Synchronization analysis of coupled noncoherent oscillators N2 - We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators Y1 - 2006 UR - http://www.springerlink.com/content/102972 U6 - https://doi.org/10.1007/s11071-006-1957-x SN - 0924-090X ER - TY - 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 -