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Amplitude death in coupled chaotic oscillators.

Awadhesh Prasad1

  • 1Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India. awadhesh@physics.du.ac.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

Amplitude death, a phenomenon where chaotic systems stabilize to fixed points, can occur in coupled chaotic systems with time-delay. This stabilization of subsystems is a general finding for both identical and nonidentical systems.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Complex systems

Background:

  • Coupled dynamical systems can exhibit complex behaviors, including synchronization and chaos.
  • Amplitude death is a known phenomenon in coupled oscillators, leading to stable states.
  • Chaotic systems present unique challenges due to their sensitive dependence on initial conditions.

Purpose of the Study:

  • To investigate the occurrence of amplitude death in chaotic dynamical systems.
  • To explore the effect of time-delay coupling on chaotic system stability.
  • To analyze transitions from chaotic dynamics to fixed points in coupled chaotic systems.

Main Methods:

  • Utilizing the Lorenz and Rössler chaotic oscillators as representative models.
  • Implementing time-delay coupling between the chaotic systems.

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  • Analyzing the system dynamics to identify fixed points and transitions.

    • Main Results:

    • Amplitude death is demonstrated in coupled chaotic systems with time-delay coupling.
    • The coupling mechanism stabilizes fixed points of the individual subsystems.
    • The phenomenon is observed in both identical and nonidentical coupled chaotic systems.
    • Various transitions from chaotic dynamics to fixed points are characterized.

    Conclusions:

    • Time-delay coupling can induce amplitude death in chaotic systems.
    • This stabilization effect is a general property applicable to diverse chaotic systems.
    • The findings extend the understanding of amplitude death beyond limit-cycle oscillators to chaotic regimes.