Explosive transitions in interacting star networks

TL;DR

This paper investigates explosive synchronization transitions in star network configurations of Stuart-Landau oscillators, revealing how coupling types and network interactions influence the nature of phase transitions.

Contribution

It introduces frequency weighted coupling and time scale variations to induce explosive synchronization and explores the effects of different inter-star coupling schemes on transition nature.

Findings

First order explosive transition observed with weighted coupling and time scale variations.

Hysteresis width varies with inter-star coupling, increasing then saturating or decreasing.

Transition becomes second order with strong symmetry-breaking coupling.

Abstract

We study 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 time scale variations in the dynamics of nodes, system exhibits a first order explosive transition to phase synchrony. Further, we extend this study to understand the nature of synchronization in case of two coupled star networks. In presence of symmetry preserving (direct) coupling between the hubs of the two stars, we observe that hysteresis width first increases and then saturates for increasing inter-star coupling strength. For symmetry breaking (conjugate) coupling, the hysteresis width first increases and then decreases with increasing inter-star coupling. As we increase the inter-star coupling further, the transition gradually becomes a second order.