Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

TL;DR

This paper develops a theoretical framework to predict phase difference distributions in uncoupled oscillators receiving common impulses, validated through numerical simulations of neural oscillators, enhancing understanding of synchronization phenomena.

Contribution

It introduces an averaging method to derive stationary phase difference distributions from phase response curves for impulse-driven oscillators.

Findings

The theory accurately predicts phase difference distributions.

Numerical simulations confirm the theoretical predictions.

The approach applies to neural oscillators with common Poisson impulses.

Abstract

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase difference from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example.