Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses

Abstract

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process describing a Poisson-driven limit-cycle oscillator, and verify the results through numerical simula- tions and electric circuit experiments. We also give a geometrical interpretation of the synchronizing mechanism, a perturbative expansion to the stationary phase distribution, and the diffusion limit of our jump stochastic model.

References in corpus (6)

• Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems
• Synchrony of limit-cycle oscillators induced by random external impulses
• On-off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics
• Reproducibility of a noisy limit-cycle oscillator induced by a fluctuating input

Cited by in corpus (11)

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• Dynamics of Limit Cycle Oscillator Subject to General Noise
• Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
• Experimental synchronization of circuit oscillations induced by common telegraph noise
• Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data
• Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization
• Coherence versus reliability of stochastic oscillators with delayed feedback
• Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise
• Criterion for noise-induced synchronization: application to colloidal alignment
• Instantaneous phase synchronization of two decoupled quantum limit-cycle oscillators induced by conditional photon detection
• Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses