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Synchronization of time-continuous chaotic oscillators.

Sergiy Yanchuk1, Yuri Maistrenko, Erik Mosekilde

  • 1Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev 01601, Ukraine. yanchuk@imath.kiev.ua

Chaos (Woodbury, N.Y.)
|April 5, 2003
PubMed
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This study analyzes synchronized chaotic oscillators, revealing how parameter mismatches and coupling asymmetry alter stability. It explores riddled basins of attraction and partial synchronization in complex systems.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Coupled chaotic oscillators exhibit complex synchronization phenomena.
  • Understanding the stability of synchronized states is crucial for predicting system behavior.
  • Riddled basins of attraction indicate sensitive dependence on initial conditions.

Purpose of the Study:

  • To establish conditions for transverse stability in synchronized chaotic oscillators.
  • To investigate the impact of parameter mismatch and coupling asymmetry on synchronization stability.
  • To explore partial synchronization in coupled chaotic systems.

Main Methods:

  • Application of periodic orbit threshold theory.
  • Analysis of bifurcations leading to loss of transverse stability.

Related Experiment Videos

  • Investigation of globally and locally riddled basins of attraction.

    • Main Results:

    • Conditions for transverse stability of the fully synchronized chaotic state are established.
    • Parameter mismatch shifts the synchronization manifold, affecting stability.
    • Coupling asymmetry further modifies the destabilization process.
    • Partial synchronization is examined in a four-oscillator system.

    Conclusions:

    • Parameter mismatch and coupling asymmetry significantly influence the stability of synchronized chaotic states.
    • The nature of bifurcations determines the type of riddled basins observed.
    • Complex dynamics, including partial synchronization, arise in coupled chaotic systems.