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Four-phase patterns in forced oscillatory systems

Lin1, Hagberg, Ardelea

  • 1Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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External periodic forcing of self-oscillating systems can create complex patterns. Researchers observed four-phase rotating spiral patterns in reaction-diffusion systems and chemical reactions, with potential transitions to standing patterns.

Area of Science:

  • Nonlinear dynamics
  • Pattern formation
  • Chemical kinetics

Background:

  • Self-oscillating systems exhibit intrinsic periodic behavior.
  • External periodic perturbations can alter system dynamics and lead to pattern formation.
  • Reaction-diffusion systems and chemical reactions are common models for studying oscillations and pattern formation.

Purpose of the Study:

  • To investigate pattern formation in self-oscillating systems under external periodic forcing.
  • To analyze the entrainment phenomena and emergent spatial patterns.
  • To explore the transition between different pattern states.

Main Methods:

  • Experimental observations of chemical systems (Belousov-Zhabotinsky reaction).
  • Numerical simulations of reaction-diffusion models (FitzHugh-Nagumo, Brusselator).

Related Experiment Videos

  • Theoretical analysis using amplitude equations for periodically forced oscillating systems.

    • Main Results:

    • Observed entrainment to rational multiples of the forcing frequency, particularly subharmonic resonance (1/4 driving frequency).
    • Identified four-phase rotating spiral patterns at low forcing amplitudes.
    • Predicted and observed a bifurcation from rotating spirals to standing patterns with increasing forcing in models.
    • Noted the absence of this transition in excitable regimes of the Belousov-Zhabotinsky system.

    Conclusions:

    • External periodic forcing is a viable method to induce and control pattern formation in oscillating systems.
    • The transition from rotating to standing patterns is a robust phenomenon predicted by amplitude equations and observed in various models.
    • System kinetics (oscillatory vs. excitable) influence the observed pattern dynamics and transitions.