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Synchronization of hyperchaotic systems with delayed bidirectional coupling.

Nikola Burić1, Dragana Todorović

  • 1Department of Physics and Mathematics, Faculty of Pharmacy, University of Beograd, Vojvode Stepe 450, Beograd, Yugoslavia. buric@phy.bg.ac.yu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 3, 2004
PubMed
Summary

Researchers analyzed the synchronization of three coupled hyperchaotic systems. A sufficient condition for global stability of exact synchronization was analytically derived, with local stability confirmed numerically.

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Area of Science:

  • Chaos theory
  • Nonlinear dynamics
  • Complex systems

Background:

  • Hyperchaotic systems exhibit complex dynamics.
  • Synchronization is crucial for understanding coupled nonlinear systems.
  • The Ikeda model is a well-known hyperchaotic system.

Purpose of the Study:

  • To investigate the synchronization of three bidirectionally coupled hyperchaotic systems.
  • To derive analytical conditions for the stability of synchronization.
  • To numerically assess the local stability of the synchronization manifold.

Main Methods:

  • Utilizing three bidirectionally coupled Ikeda hyperchaotic systems.
  • Formulating the system using delay-differential equations with two time lags.
  • Analytical derivation of the sufficient condition for global synchronization stability.

Related Experiment Videos

  • Numerical computation of transverse Lyapunov exponents and statistical orbit properties for local stability analysis.

    • Main Results:

    • A sufficient condition for the global stability of the exact synchronization manifold was analytically determined.
    • Numerical analysis confirmed the local stability of the synchronization manifold.
    • The study provides insights into the synchronization behavior of complex coupled systems.

    Conclusions:

    • The derived analytical condition guarantees global synchronization stability for the studied system.
    • Numerical methods validate the findings and confirm local stability.
    • This research contributes to the understanding of synchronization in complex, coupled chaotic systems.