Cluster Explosive Synchronization in Complex Networks
Peng Ji, Thomas K.DM. Peron, Peter J. Menck, Francisco A. Rodrigues,, and J\"urgen Kurths

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.
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