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Cluster Explosive Synchronization in Complex Networks
Peng Ji, Thomas K. DM. Peron, Peter J. Menck, Francisco A. Rodrigues, Jürgen Kurths
TL;DR
Explosive synchronization in first-order networks does not capture the cascade of node transitions found here in a second-order Kuramoto model. Using mean-field analysis for uncorrelated networks, the paper identifies cluster explosive synchronization, with theory agreeing well with simulations.
Problem
The paper addresses how explosive synchronization develops in second-order Kuramoto networks when natural frequency is proportional to node degree.
Method
The authors develop a mean-field theory for uncorrelated networks and derive self-consistent equations for synchronization thresholds and synchronized degrees.
Results
Nodes of equal degree join the synchronous component successively from small degrees, producing cluster explosive synchronization and hysteretic synchronization thresholds consistent with simulations.
Takeaways & Limitations
The findings deepen understanding of microscopic synchronization mechanisms and provide an analytical treatment that can be extended to applications using second-order Kuramoto oscillators.
Takeaways & Limitations
The mean-field analysis assumes zero degree correlation, and its self-consistent treatment approximates C(λr) from simulated mean-field dynamics before and after synchronization.
Abstract
from arXiv · showhide
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.