Modular synchronization in complex networks

Details Modular synchronization in complex networks Modular synchronization in complex networks

2004-08-10

arxiv.org/abs/cond-mat/0408202v2

Physics

Condensed Matter

Statistical Mechanics

9pages, 6figures. PRE (in press)

Scientific paper

10.1103/PhysRevE.72.047101

We study the synchronization transition (ST) of a modified Kuramoto model on two different types of modular complex networks. It is found that the ST depends on the type of inter-modular connections. For the network with decentralized (centralized) inter-modular connections, the ST occurs at finite coupling constant (behaves abnormally). Such distinct features are found in the yeast protein interaction network and the Internet, respectively. Moreover, by applying the finite-size scaling analysis to an artificial network with decentralized inter-modular connections, we obtain the exponent associated with the order parameter of the ST to be $\beta \approx 1$ different from $\beta_{\rm MF} \approx 1/2$ obtained from the scale-free network with the same degree distribution but the absence of modular structure, corresponding to the mean field value.

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