Synchronization of frustrated phase oscillators in the small-world networks

TL;DR

This study investigates how phase-shift influences synchronization in small-world networks of identical oscillators, revealing enhanced synchronization, explosive transitions, and Chimera states near transition points.

Contribution

It demonstrates that phase-shift can enhance synchronization and induce explosive transitions and Chimera states in small-world networks, a novel insight into network dynamics.

Findings

Phase-shift enhances synchronization in small-world networks.

Abrupt phase transitions with hysteresis occur at certain phase-shift values.

Chimera states emerge near transition points.

Abstract

We numerically study the synchronization of an identical population of Kuramoto-Sakaguchi phase oscillators in Watts-Strogatz networks. We find that, unlike random networks, phase-shift could enhance the synchronization in small-world networks. We also observe abrupt phase transition with hysteresis at some values of phase shifts in small-world networks, signs of an explosive phase transition. Moreover, we report the emergence of Chimera states at some values of phase-shift close to the transition points, which consist of spatially coexisting synchronized and desynchronized domains.