Synchronization of Kuramoto Oscillators in Scale-Free Networks

TL;DR

This paper investigates how Kuramoto oscillators synchronize on scale-free networks, analyzing the onset of synchronization, system dynamics, and how node connectivity influences resynchronization time.

Contribution

It provides a detailed characterization of synchronization phenomena on scale-free networks and explains the power-law decay of resynchronization time based on node connectivity.

Findings

Synchronization onset depends on network topology.

Resynchronization time decays as a power law with connectivity.

Analytical explanation for resynchronization behavior.

Abstract

In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others following the Kuramoto model. We then study the onset of global phase synchronization and fully characterize the system's dynamics. We also found that the resynchronization time of a perturbed node decays as a power law of its connectivity, providing a simple analytical explanation to this interesting behavior.