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Generalized synchronization in time-delayed systems.

E M Shahverdiev1, K A Shore

  • 1Institute of Physics, 33, H. Javid Avenue, 370143-Baku, Azerbaijan. shahverdiev@physics.ab.az

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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This study explores chaos synchronization in coupled Ikeda models, establishing conditions for generalized synchronization and stability in systems with variable delays. The findings extend to a broader range of nonlinear chaotic systems.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Coupled chaotic systems exhibit complex behaviors, including synchronization.
  • The Ikeda model is a canonical system for studying nonlinear dynamics and chaos.
  • Understanding synchronization in nonidentical systems with delays is crucial for various applications.

Purpose of the Study:

  • To investigate generalized synchronization in unidirectionally coupled, nonidentical Ikeda models.
  • To determine the existence conditions for generalized synchronization under linear and nonlinear coupling.
  • To analyze chaos synchronization in Ikeda models with variable feedback-delay times and coupling-delay lag time.

Main Methods:

  • Analysis of coupled Ikeda models with unidirectional linear and nonlinear coupling.

Related Experiment Videos

  • Derivation of existence conditions for generalized synchronization.
  • Investigation of systems with variable feedback-delay and coupling-delay lag times.
  • Stability analysis of the retarded synchronization manifold.

    • Main Results:

    • Existence conditions for generalized synchronization were found for linearly and nonlinearly coupled nonidentical Ikeda models.
    • Sufficient stability conditions for the retarded synchronization manifold were established for systems with variable feedback-delay times.
    • The developed approach was generalized to a wide class of nonlinear chaotic systems.

    Conclusions:

    • Generalized synchronization can be achieved in coupled nonidentical Ikeda models under specific conditions.
    • Variable feedback-delay times and coupling-delay lag times influence the stability of chaos synchronization.
    • The presented methodology offers a versatile framework for analyzing synchronization in diverse nonlinear chaotic systems.