Chapter 12. Phase Synchronization of Regular and Chaotic Oscillators

  1. Heinz G. Schuster
  1. A. S. Pikovsky,
  2. M. G. Rosenblum,
  3. M. A. Zaks and
  4. J. Kurths

Published Online: 31 MAY 2006

DOI: 10.1002/3527607455.ch12

Handbook of Chaos Control

Handbook of Chaos Control

How to Cite

Pikovsky, A. S., Rosenblum, M. G., Zaks, M. A. and Kurths, J. (1999) Phase Synchronization of Regular and Chaotic Oscillators, in Handbook of Chaos Control (ed H. G. Schuster), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527607455.ch12

Editor Information

  1. University of Kiel, Institute of Theoretical Physics, Leibnizstr. 15, D-24098 Kiel, Germany

Author Information

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

Publication History

  1. Published Online: 31 MAY 2006
  2. Published Print: 23 FEB 1999

ISBN Information

Print ISBN: 9783527294367

Online ISBN: 9783527607457



  • phase synchronization;
  • chaotic oscillators;
  • external force;
  • embedded periodic orbits;
  • coupled systems;
  • detecting synchronization


This chapter contains sections titled:

  • Introduction

  • Synchronization of periodic oscillations

  • Phase of a chaotic oscillator

    • Definition of the phase

    • Dynamics of the phase of chaotic oscillations

  • Phase synchronization by external force

    • Synchronization region

    • Statistical approach

    • Interpretation through embedded periodic orbits

  • Phase synchronization in coupled systems

    • Synchronization of two interacting oscillators

    • Synchronization in a Population of Globally Coupled Chaotic Oscillators

  • Lattice of chaotic oscillators

  • Synchronization of space-time chaos

  • Detecting synchronization in data

  • Conclusions