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- P Tass, M G Rosenblum, J Weule, J Kurths, A Pikovsky, J Volkmann +2 others
- 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)

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.

- P C Ivanov, L A Amaral, A L Goldberger, S Havlin, M G Rosenblum, Z R Struzik +1 other
- Nature
- 1999

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their… (More)

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)

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)

We investigate synchronization between cardiovascular and respiratory systems in healthy humans under free-running conditions. For this aim we analyze nonstationary irregular bivariate data, namely, electrocardiograms and measurements of respiratory flow. We briefly discuss a statistical approach to synchronization in noisy and chaotic systems and… (More)