Mobility induces global synchronization of oscillators in periodic extended systems

TL;DR

This paper investigates how mobility influences the synchronization of noisy phase oscillators in a ring, revealing a critical diffusion threshold that destabilizes wave-like states and promotes global synchronization.

Contribution

It introduces a statistical framework for large oscillator systems and demonstrates how spatial diffusion destabilizes wave states, leading to synchronization.

Findings

Existence of a critical diffusion threshold for stability of wave states

Spatial diffusion destabilizes wave-like solutions

Transition to global synchronization depends on attractor basin sizes

Abstract

We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which display local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical spatial diffusion above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by the relative size of attractor basins associated to wave-like states. Spatial diffusion disrupts these states and paves the way for the system to attain global synchronization.