Synchronization transition in scale-free networks: Clusters of synchrony

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 $\lambda>3$.