Synchronization failure caused by interplay between noise and network heterogeneity

TL;DR

This paper explores how noise and network heterogeneity interact to cause synchronization failure in complex oscillator networks, revealing an optimal intermediate coupling range for synchronization.

Contribution

It uncovers the interplay between noise, coupling strength, and heterogeneity as a cause of synchronization failure, and explains the phenomenon through analysis of phase slip behavior.

Findings

Synchronization occurs only within a narrow coupling range.

Strong coupling induces phase slips leading to failure.

Heterogeneity narrows the synchronization window.

Abstract

We investigate synchronization in complex networks of noisy phase oscillators. We find that, while too weak a coupling is not sufficient for the whole system to synchronize, too strong a coupling induces a nontrivial type of phase slip among oscillators, resulting in synchronization failure. Thus, an intermediate coupling range for synchronization exists, which becomes narrower when the network is more heterogeneous. Analyses of two noisy oscillators reveal that nontrivial phase slip is a generic phenomenon when noise is present and coupling is strong. Therefore, the low synchronizability of heterogeneous networks can be understood as a result of the difference in effective coupling strength among oscillators with different degrees; oscillators with high degrees tend to undergo phase slip while those with low degrees have weak coupling strengths that are insufficient for synchronization.