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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Theoretical physics

Background:

  • Coupled oscillators are fundamental in many natural and engineered systems.
  • Synchronization phenomena are well-studied, but instabilities in noisy systems remain challenging.
  • Averaged models like the Kuramoto model simplify oscillator dynamics but may miss crucial details.

Purpose of the Study:

  • To investigate a synchronization-breaking instability in a noisy oscillator unidirectionally coupled to a pacemaker.
  • To analyze the behavior of phase slips and their dependence on coupling strength.
  • To identify the conditions leading to a reentrant transition between synchronized and phase slip states.

Main Methods:

  • Utilized a phase oscillator model to simulate the coupled system.
  • Analyzed the corresponding Fokker-Planck equation to derive theoretical predictions.
  • Verified the theoretical findings using the Brusselator model, a representative limit cycle oscillator.

Main Results:

  • Observed a synchronization-breaking instability as coupling strength increased.
  • Found that the noisy oscillator lags behind the pacemaker more frequently, increasing the phase slip rate.
  • Derived the reentrant transition line separating synchronized and phase slip states.

Conclusions:

  • The study reveals a synchronization-breaking instability in noisy coupled oscillators.
  • Phase slip dynamics and reentrant transitions are crucial and may be missed by averaged models.
  • The findings are applicable to a broad range of limit cycle oscillators, including the Brusselator model.