Synchronization transition in scale-free networks: Clusters of synchrony

TL;DR

This paper investigates how the structural properties of scale-free networks influence the emergence and nature of synchronization transitions, revealing different behaviors depending on the degree exponent.

Contribution

It provides a mean field analysis of the critical coupling and finite-size scaling in scale-free networks, highlighting the role of degree exponent in synchronization dynamics.

Findings

Critical coupling strength depends on degree exponent λ.

Different formation mechanisms of synchronized clusters for 2<λ<3 and λ>3.

Finite-size scaling behavior varies with network degree distribution.

Abstract

We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field approach depend on the degree exponent $\lambda$, which implies a close connection between structural organization and the emergence of dynamical order in complex systems. We also derive the finite-size scaling behavior of the order parameter finding that the giant cluster of synchronized nodes is formed in different ways between scale-free networks with $2<\lambda<3$ and those with $\lambda>3$.