Explosive synchronization in interacting star networks

Abstract

We study the transition to phase synchronization in an ensemble of Stuart–Landau oscillators interacting on a star network. We observe that by introducing frequency-weighted coupling and timescale variations in the dynamics of nodes, the system exhibits a first-order explosive transition to phase synchrony. Further, we extend this study to understand the nature of synchronization in the case of two coupled star networks. If the coupled star networks are identical, we observe that with increasing inter-star coupling strength, the hysteresis width initially increases, reaches a maximum value, then decreases before saturating. If the interacting star networks are non-identical, we observe that the transition to the coherent state is preceded by the occurrence of intermittent in-phase and anti-phase synchrony for small inter-star coupling. However, for large values of coupling strengths, we observe that the intermittent state disappears and the hysteresis width changes as in coupled identical star networks. We characterize these transitions by plotting the Lyapunov exponents for the system and the master stability function.