Chapter 10. Synchronization in Chaotic Systems, Concepts and Applications

  1. Heinz G. Schuster
  1. L. M. Pecora1,
  2. T. L. Carroll1 and
  3. J. F. Heagy2

Published Online: 31 MAY 2006

DOI: 10.1002/3527607455.ch10

Handbook of Chaos Control

Handbook of Chaos Control

How to Cite

Pecora, L. M., Carroll, T. L. and Heagy, J. F. (1999) Synchronization in Chaotic Systems, Concepts and Applications, in Handbook of Chaos Control (ed H. G. Schuster), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527607455.ch10

Editor Information

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

Author Information

  1. 1

    Code 6343, Naval Research Laboratory, Washington, DC 20375, USA

  2. 2

    Computer Sciences Corporation, System Sciences Division, GT II, 10110 Aerospace Road, Lanham, MD 20706, USA

Publication History

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

ISBN Information

Print ISBN: 9783527294367

Online ISBN: 9783527607457



  • synchronization in chaotic systems;
  • geometry of synchronization;
  • identical synchronization;
  • transverse manifold;
  • synchronous circuits;
  • bifurcations;
  • mutually coupled chaotic systems;
  • coupling thresholds;
  • bursting;
  • hyperchaos synchronization


This chapter contains sections titled:

  • Introduction and Motivation

  • The Geometry of Synchronization

    • Simple Examples

    • Some Generalizations and a Definition of Identical Synchronization

  • The Dynamics of Synchronization

    • Stability and the Transverse Manifold

    • Synchronizing Chaotic Systems, Variations on Themes

  • Synchronous Circuits and Applications

  • Stability and Bifurcations of Synchronized, Mutually Coupled Chaotic Systems

    • Stability for Coupled, Chaotic Systems

    • Coupling Thresholds for Synchronized Chaos and Bursting

    • Desynchronization Thresholds at Increased Coupling

    • Size Limits on Certain Chaotic Synchronized Arrays

    • Riddled Basins of Synchronization

  • Transformations, Synchronization, and Generalized Synchronization

    • Synchronizing with Functions of the Dynamical Variables

    • Hyperchaos Synchronization

    • Generalized Synchronization