Interplay of coupling and common noise at the transition to synchrony in oscillator populations

TL;DR

This paper analyzes how coupling and common noise influence the transition to synchrony in oscillator populations, revealing that noise promotes synchronization while repulsive coupling can oppose it, with complex effects depending on oscillator heterogeneity.

Contribution

It provides an analytical framework using the Ott-Antonsen ansatz to understand the interplay of noise and coupling in oscillator synchronization, including effects of frequency dispersion.

Findings

Noise always promotes synchronization.

Repulsive coupling can oppose synchrony.

Frequency dispersion affects the stability of synchronized states.

Abstract

We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the order parameter. While noise always tends to synchronize the oscillators, the coupling can act against synchrony if it is repulsive. For identical oscillators, the fully synchronous state remains stable for small enough repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion of the oscillators frequencies at synchrony.