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Robust synchronization of chaotic systems.

L Kocarev1, U Parlitz, R Brown

  • 1Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Robust chaos synchronization ensures smooth system behavior under small perturbations. However, normal hyperbolicity alone doesn't prevent large synchronization errors in real-world applications.

Area of Science:

  • Dynamical Systems Theory
  • Chaos Synchronization
  • Nonlinear Dynamics

Background:

  • Investigating the robustness of synchronization in dynamical systems is crucial for practical applications.
  • Understanding how systems maintain synchronized behavior under perturbations is a key challenge.

Purpose of the Study:

  • To address the robustness of chaos synchronization against small arbitrary perturbations.
  • To determine the conditions for a smooth and persistent synchronization manifold.

Main Methods:

  • Analysis of chaos synchronization examples.
  • Demonstration of necessary and sufficient conditions for manifold properties.

Main Results:

  • Normal hyperbolicity is identified as a necessary and sufficient condition for a smooth and persistent synchronization manifold under small perturbations.

Related Experiment Videos

  • Examples show that normal hyperbolicity does not provide quantitative bounds for synchronization manifold deformations.
  • Near-identical systems can exhibit significant synchronization errors even with normal hyperbolicity.

    • Conclusions:

    • While normal hyperbolicity guarantees the existence of a smooth synchronization manifold, it does not suffice for controlling synchronization errors in practical scenarios.
    • Further research is needed to establish quantitative measures for synchronization robustness in the presence of perturbations.