Effect of mobility on synchronization of nonlocally coupled oscillators with a phase lag

TL;DR

This paper studies how mobility influences the synchronization patterns of nonlocally coupled oscillators with phase lag, revealing that mobility can either promote or destroy synchronization depending on the coupling type, and uncovers a new spatiotemporal pattern.

Contribution

It introduces a model where oscillators move on a ring with phase lag, analyzing the combined effects of mobility and phase lag on collective dynamics, including a novel pattern at the transition.

Findings

Mobility promotes synchronization with attractive coupling.

Mobility destroys coherence with repulsive coupling.

A new spatiotemporal pattern emerges at the boundary between states.

Abstract

Nonlocally coupled oscillators with a phase lag self-organize into various patterns such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors, and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, while it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states.