Interplay of noise and coupling in heterogeneous ensembles of phase oscillators

TL;DR

This paper investigates how heterogeneous noise and coupling strengths influence the synchronization of identical phase oscillators, revealing conditions under which noise-induced desynchronization can be suppressed.

Contribution

It introduces a comprehensive analysis of the combined effects of heterogeneous noise and coupling on oscillator synchronization, including conditions that prevent desynchronization.

Findings

Desynchronization can be suppressed if the coupling strength distribution decays slowly.

Weak responses to noise in a large part of the ensemble prevent desynchronization.

Correlation between noise response and coupling strength significantly affects collective dynamics.

Abstract

We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise can also be heterogeneous, representing diversity in the individual responses to external fluctuations. We show that the desynchronization transition induced by noise may be completely suppressed, even for arbitrarily large noise intensities, is the distribution of coupling strengths decays slowly enough for large couplings. Equivalently, if the response to noise of a sufficiently large fraction of the ensemble is weak enough, desynchronization cannot occur. The two effects combine with each other when the response to noise and the coupling strength of each oscillator are correlated. This combination is quantitatively characterized and illustrated with explicit examples.