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Explosive Synchronization Transitions in Scale-free Networks
Jesus Gomez-Gardenes, Sergio Gomez, Alex Arenas, Yamir Moreno
TL;DR
The paper asks whether explosive transitions can arise in synchronization and links them to correlations between network structure and oscillator dynamics. It studies Kuramoto oscillators on scale-free networks and analytically examines the transition in a star graph, finding an abrupt transition when natural frequencies positively correlate with node degrees.
Problem
Scale-free network topology had not been shown to change synchronization from its usual second-order character, while the microscopic mechanisms of explosive transitions remained open.
Method
The paper identifies each oscillator’s natural frequency with its node degree, simulates correlated Kuramoto dynamics on interpolated and scale-free networks, breaks the correlation as a control, and analyzes a star graph analytically.
Results
Positive degree-frequency correlation produces a first-order synchronization transition in scale-free networks, with abrupt locking and hysteresis; randomizing frequencies restores second-order transitions.
Takeaways & Limitations
Explosive synchronization arises from the interplay between heterogeneous local structure and positively correlated internal dynamics, rather than from the natural-frequency distribution alone.
Takeaways & Limitations
The analysis assumes a unimodal and even natural-frequency distribution.
Abstract
from arXiv · showhide
The emergence of explosive collective phenomena has recently attracted much attention due to the discovery of an explosive percolation transition in complex networks. In this Letter, we demonstrate how an explosive transition shows up in the synchronization of complex heterogeneous networks by incorporating a microscopic correlation between the structural and the dynamical properties of the system. The characteristics of this explosive transition are analytically studied in a star graph reproducing the results obtained in synthetic scale-free networks. Our findings represent the first abrupt synchronization transition in complex networks thus providing a deeper understanding of the microscopic roots of explosive critical phenomena.