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

TL;DR

This paper develops a theoretical framework to understand how common Poisson impulses influence synchronization, desynchronization, and clustering in uncoupled limit-cycle oscillators, supported by simulations and experiments.

Contribution

It introduces a phase reduction theory for Poisson-driven oscillators and provides geometric, perturbative, and diffusion analyses of their collective behavior.

Findings

The theory predicts diverse group behaviors under common impulses.

Numerical simulations and experiments confirm the theoretical predictions.

The paper offers a geometric interpretation of synchronization mechanisms.

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.