Phase coherence induced by correlated disorder

TL;DR

This paper investigates how correlated disorder in coupling strengths and natural frequencies of coupled phase oscillators can induce phase coherence and synchronization, contrasting with uncorrelated disorder where coherence is absent.

Contribution

It introduces a mean-field model with correlated disorder, demonstrating that such correlations can lead to spontaneous synchronization or traveling wave states.

Findings

Correlated disorder induces phase coherence below a critical frequency width.

Symmetric correlation leads to spontaneous synchronization.

Asymmetric correlation results in coherent traveling waves.

Abstract

We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal in number and strength), it is known that phase coherence cannot occur and synchronization is absent. Here we explore the effects of correlating the disorder. Specifically, we assume that any given oscillator either attracts or repels all the others, and that the sign of the interaction is deterministically correlated with the given oscillator's natural frequency. For symmetrically correlated disorder with zero mean, we find that the system spontaneously synchronizes, once the width of the frequency distribution falls below a critical value. For asymmetrically correlated disorder, the model displays coherent traveling waves: the complex order parameter becomes nonzero and rotates with constant frequency different from the system's mean natural frequency. Thus, in both cases, correlated disorder can trigger phase coherence.