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Related Experiment Videos

Phase synchronization in coupled chaotic oscillators with time delay.

J Y Chen1, K W Wong, J W Shuai

  • 1Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
Summary

Time delay consistently induces phase synchronization (PS) in coupled Rössler oscillators. Increasing delay alters coupling strength thresholds, revealing complex synchronization patterns and re-emergence of PS.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems analysis
  • Coupled oscillator theory

Background:

  • Phase synchronization (PS) is a fundamental phenomenon in coupled nonlinear systems.
  • Understanding the influence of time delays on PS is crucial for complex systems.
  • Rössler oscillators are a standard model for studying chaotic dynamics.

Purpose of the Study:

  • To investigate the effect of time-delayed signal coupling on phase synchronization in two Rössler oscillators.
  • To characterize the relationship between time delay, coupling strength, and the onset of PS.
  • To explore novel synchronization phenomena induced by time delays.

Main Methods:

  • Numerical simulation of two coupled Rössler oscillators.
  • Systematic variation of time delay and coupling strength parameters.

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  • Analysis of phase dynamics to identify transitions to phase synchronization.

    • Main Results:

    • Time delay was found to reliably induce phase synchronization, irrespective of delay length.
    • The critical coupling strength for PS exhibited a nearly periodic dependence on time delay.
    • Complex synchronization behaviors were observed, including alternating PS and non-PS regions with increasing coupling strength.

    Conclusions:

    • Time-delayed coupling is a robust mechanism for achieving phase synchronization in Rössler systems.
    • The interplay between time delay and coupling strength leads to intricate synchronization patterns.
    • The findings offer insights into the control and understanding of synchronization in delayed dynamical systems.