Phase coherence induced by correlated disorder

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.

6 pages, 6 figures

References in corpus (2)

• The Kuramoto model in complex networks
• Frequency assortativity can induce chaos in oscillator networks

Cited by in corpus (5)

• Oscillators that sync and swarm
• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
• Generic criterion for explosive synchronization in heterogeneous phase oscillator populations
• Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations
• A Two-Frequency-Two-Coupling model of coupled oscillators