Cluster Explosive Synchronization in Complex Networks

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 $\mathit{\text{cluster}}\mathit{\text{explosive}}\mathit{\text{synchronization}}$. 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.