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Phase Synchronization of Regular and Chaotic Self-Sustained Oscillators

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Synchronization: Theory and Application

Part of the book series: NATO Science Series ((NAII,volume 109))

Abstract

In this review article we discuss effects of phase synchronization of nonlinear self-sustained oscillators. Starting with a classical theory of phase locking, we extend the notion of phase to autonoumous continuous-time chaotic systems. Using as examples the well-known Lorenz and R ö ssler oscillators, we describe the phase synchronization of chaotic oscillators by periodic external force. Both statistical and topological aspects of this phenomenon are discussed. Then we proceed to more complex cases and discuss phase synchronization in coupled systems, lattices, large globally coupled ensembles, and of space-time chaos. Finally, we demonstrate how the synchronization effects can be detected from observations of real data.

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Authors and Affiliations

  1. Department of Physics, Potsdam University, Am Neuen Palais 19, PF 601553, D-14415, Potsdam, Germany

    Arkady S. Pikovsky & Michael G. Rosenblum

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  1. Arkady S. Pikovsky
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  2. Michael G. Rosenblum
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  1. University of Potsdam, Potsdam, Germany

    Arkady Pikovsky

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Yuri Maistrenko

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Pikovsky, A.S., Rosenblum, M.G. (2003). Phase Synchronization of Regular and Chaotic Self-Sustained Oscillators. In: Pikovsky, A., Maistrenko, Y. (eds) Synchronization: Theory and Application. NATO Science Series, vol 109. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0217-2_9

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  • DOI: https://doi.org/10.1007/978-94-010-0217-2_9

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