Explosive synchronization transition in a ring of coupled oscillators

TL;DR

This paper investigates explosive synchronization in a ring of coupled oscillators, showing how coupling weight influences the transition from partial to explosive synchronization and the hysteresis behavior.

Contribution

It introduces a mixed explosive synchronization phenomenon in a ring of oscillators and analyzes how coupling weight controls the transition and hysteresis region.

Findings

Coupling weight affects the size of the hysteresis region.

Transition varies from mixed ES to ES to continuous with increasing coupling.

Theoretical analysis explains the transition behavior.

Abstract

Explosive synchronization(ES), as one kind of abrupt dynamical transition in nonlinearly coupled systems, is currently a subject of great interests. Given a special frequency distribution, a mixed ES is observed in a ring of coupled phase oscillators which transit from partial synchronization to ES with the increment of coupling strength. The coupling weight is found to control the size of the hysteresis region where asynchronous and synchronized states coexist. Theoretical analysis reveals that the transition varies from the mixed ES, to the ES and then to a continuous one with increasing coupling weight. Our results are helpful to extend the understanding of the ES in homogenous networks.