Synchronization transition in scale-free networks: Clusters of synchrony

Details Synchronization transition in scale-free networks: Clusters of synchrony Synchronization transition in scale-free networks: Clusters of synchrony

2004-10-25

arxiv.org/abs/cond-mat/0410635v2

Phys. Rev. E 72, 026208 (2005)

Physics

Condensed Matter

Statistical Mechanics

3 figures, final version

Scientific paper

10.1103/PhysRevE.72.026208

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 $\lambda>3$.

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