Finite-size scaling of synchronized oscillation on complex networks

Abstract

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution $P(k)\sim k^{-\gamma }$ at large $k$, we found that the finite size exponent $\bar{\nu }$ takes on the value 5/2 when $\gamma >5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks ($3<\gamma <5$), $\bar{\nu }$ and the order parameter exponent $\beta$ depend on $\gamma$. The analytic expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations.

7 pages

References in corpus (3)

• Finite-size scaling in complex networks
• Synchronization transition in scale-free networks: Clusters of synchrony
• Entrainment transition in populations of random frequency oscillators

Cited by in corpus (1)

• Critical phenomena in complex networks