Phase Synchronization of Chaotic Oscillators

Michael G. Rosenblum, Arkady S. Pikovsky, and Jürgen Kurths
Phys. Rev. Lett. 76, 1804 – Published 11 March 1996
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Abstract

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 practically uncorrelated. Coupling a chaotic oscillator with a hyperchaotic one, we observe another new type of synchronization, where the frequencies are entrained, while the phase difference is unbounded. A relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.

  • Received 7 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.1804

©1996 American Physical Society

Authors & Affiliations

Michael G. Rosenblum, Arkady S. Pikovsky, and Jürgen Kurths

  • Max-Plank-Arbeitsgruppe “Nichtlineare Dynamik” an der Universität Potsdam, Am Neuen Palais 19, PF 601553, D-14415, Potsdam, Germany

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Issue

Vol. 76, Iss. 11 — 11 March 1996

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