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Synchronization transition in scale-free networks: Clusters of synchrony

Deok-Sun Lee
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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 $λ$, 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 $2<λ<3$ and those with $λ>3$.

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Deok-Sun Lee. 2005-08-17. Synchronization transition in scale-free networks: Clusters of synchrony. https://doi.org/10.1103/physreve.72.026208

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