Explosive synchronization in coupled stars

TL;DR

This paper investigates how network topology influences explosive synchronization in coupled star networks of Kuramoto oscillators, revealing that inter-star coupling strength affects hysteresis width and transition points independently of network size.

Contribution

It introduces a model of multiple coupled star networks demonstrating how inter-star coupling impacts explosive synchronization and hysteresis, supported by WS theory analysis.

Findings

Hysteresis width increases with inter-star coupling strength.

Backward transition point is independent of number of stars and coupling strength.

Results are consistent across different network sizes.

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 study, 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 inter-star coupling strength, the hysteresis width between the forward and backward transition point is minimal, which increases with an increase in the inter-star 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 inter-star coupling strength, which is also verified using the Watanabe and Strogatz (WS) theory.