Synchronization of frustrated phase oscillators in the small-world networks

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.