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Stochastic switching in delay-coupled oscillators.

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Summary
This summary is machine-generated.

Delay in coupled oscillators induces multistability. Noise allows switching between orbits, with frequency distributions and residence times analytically computed for phase oscillators, revealing key scaling laws.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Theoretical physics

Background:

  • Periodic systems with delays can exhibit multistability.
  • Noise can induce switching between coexistent oscillatory states in coupled systems.

Purpose of the Study:

  • To analytically investigate multistability in delay-coupled oscillators under noise influence.
  • To determine how delay and coupling strength affect orbit switching and residence times.

Main Methods:

  • Reduction of a delay system to a nondelayed Langevin equation for coupled phase oscillators.
  • Analytical computation of frequency distributions and residence times.
  • Investigation of detuning effects and demonstration with FitzHugh-Nagumo oscillators.

Main Results:

  • The number of stable periodic orbits scales with delay time and coupling strength.
  • The fraction of visited orbits scales with the square root of delay time, independent of coupling strength.
  • Residence times are primarily determined by coupling strength and oscillator number, weakly by delay.

Conclusions:

  • Delay-coupled oscillators exhibit noise-induced multistability with predictable scaling behaviors.
  • The interplay between delay, coupling, and noise governs the dynamics of visited orbits and their stability.
  • The findings are generalizable across different oscillatory models, including FitzHugh-Nagumo oscillators.