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Phase-flip bifurcation induced by time delay.

Awadhesh Prasad1, Jürgen Kurths, Syamal Kumar Dana

  • 1Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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We discovered a phase-flip bifurcation in coupled nonlinear oscillators. Time-delay coupling causes a sudden phase jump and frequency change, impacting various dynamics like oscillator death and chaos.

Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Oscillator Networks

Background:

  • Coupled nonlinear oscillators exhibit complex synchronized behaviors.
  • Time delays in coupling can significantly alter system dynamics.
  • Understanding bifurcations is crucial for predicting system transitions.

Purpose of the Study:

  • To introduce and analyze a general phase-flip bifurcation in time-delay-coupled nonlinear oscillators.
  • To investigate the conditions and consequences of this bifurcation.
  • To explore the relevance across different dynamical regimes.

Main Methods:

  • Mathematical analysis of nonlinear oscillator models with time-delayed coupling.
  • Identification of the phase-flip bifurcation point.

Related Experiment Videos

  • Numerical illustration and analytical derivation for paradigmatic systems.

    • Main Results:

    • A general phase-flip bifurcation occurs where the relative phase jumps from 0 to pi.
    • This bifurcation is accompanied by a discontinuous change in synchronized frequency.
    • Time-delay coupling is a necessary condition for this phenomenon.

    Conclusions:

    • The phase-flip bifurcation is a fundamental transition in time-delay-coupled systems.
    • It occurs across periodic, quasiperiodic, chaotic dynamics, and oscillator death regimes.
    • This finding has implications for diverse applications involving coupled oscillators.