Cluster Explosive Synchronization in Complex Networks

TL;DR

This paper introduces 'cluster explosive synchronization' in second-order Kuramoto networks, revealing a cascade of transitions to synchronization, supported by analytical and numerical evidence, advancing understanding of synchronization mechanisms.

Contribution

It is the first to identify and analyze cluster explosive synchronization in second-order Kuramoto models, expanding the knowledge of synchronization phenomena.

Findings

Demonstrates cascade of transitions to synchronization.

Provides mean-field analytical framework.

Numerical simulations confirm theoretical predictions.

Abstract

The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade of transitions toward a synchronous macroscopic state, which is a novel phenomenon that we call \textit{cluster explosive synchronization}. We provide a rigorous analytical treatment using a mean-field analysis in uncorrelated networks. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.