Explosive synchronization in coupled stars

Abstract

We study the effect of network topology on the collective dynamics of an oscillator ensemble. Specifically, we explore explosive synchronization in a system of interacting star networks. Explosive synchronization is characterized by an abrupt transition from an incoherent state to a coherent state. In this paper, we couple multiple star networks through their hubs and study the emergent dynamics as a function of coupling strength. The dynamics of each node satisfies the equation of a Kuramoto oscillator. We observe that for a small interstar coupling strength, the hysteresis width between the forward and backward transition point is minimal, which increases with an increase in the interstar coupling strength. This observation is independent of the size of the network. Further, we find that the backward transition point is independent of the number of stars coupled together and the interstar coupling strength, which is also verified using the Watanabe and Strogatz theory.

Keywords: Collective dynamics, Coupled oscillators, Dynamics of networks, Synchronization, Synchronization transition