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First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering, and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons, and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common… (More)

- P. Tass, M. G. Rosenblum, +4 authors A. Schnitzler
- 1998

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… (More)

We present the new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators. To characterize this phenomenon, we use the analytic signal approach based on the Hilbert transform and partial Poincaré maps. For coupled Rössler attractors, in the synchronous regime the phases are locked, while the amplitudes vary chaotically and are… (More)

Synchronization of coupled oscillating systems means appearance of certain relations between their phases and frequencies. Here we use this concept in order to address the inverse problem and to reveal interaction between systems from experimental data. We discuss how the phases and frequencies can be estimated from time series and present techniques for… (More)

- M G Rosenblum, A S Pikovsky
- Physical review. E, Statistical, nonlinear, and…
- 2001

We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.

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,… (More)

- Michael G Rosenblum, Laura Cimponeriu, Anastasios Bezerianos, Andreas Patzak, Ralf Mrowka
- Physical review. E, Statistical, nonlinear, and…
- 2002

We consider the problem of experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. We further develop the method introduced by Rosenblum and Pikovsky [Phys. Rev. E 64, 045202 (2001)], suggesting an alternative approach. Next, we consider another framework for identification of directionality,… (More)

- Arkady S. Pikovsky, Michael G. Rosenblum, Grigory V. Osipov, Jtirgen Kurths
- 1997

We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed, and the phase dynamics of a single self-sustained chaotic oscillator subjected to external force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the external… (More)

- Michael Rosenblum, Arkady Pikovsky
- Physical review. E, Statistical, nonlinear, and…
- 2004

We suggest a method for suppression of synchrony in a globally coupled oscillator network, based on the time-delayed feedback via the mean field. Having in mind possible applications for suppression of pathological rhythms in neural ensembles, we present numerical results for different models of coupled bursting neurons. A theory is developed based on the… (More)

PACS. 05.45+b – Theory and models of chaotic systems. PACS. 64.60Cn – Order-disorder and statistical mechanics of model systems. Abstract. – We demonstrate synchronization transition in a large ensemble of non-identical chaotic oscillators, globally coupled via the mean field. We show that this coherent behaviour is due to synchronization of phases of these… (More)