Synchronization on community networks

Details Synchronization on community networks Synchronization on community networks

2006-04-30

arxiv.org/abs/cond-mat/0605024v2

Physics Letters A 368, 431-434 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 figures and 4 pages

Scientific paper

10.1016/j.physleta.2007.04.083

In this Letter, we propose a growing network model that can generate scale-free networks with a tunable community strength. The community strength, $C$, is directly measured by the ratio of the number of external edges to internal ones; a smaller $C$ corresponds to a stronger community structure. According to the criterion obtained based on the master stability function, we show that the synchronizability of a community network is significantly weaker than that of the original Barab\'asi-Albert network. Interestingly, we found an unreported linear relationship between the smallest nonzero eigenvalue and the community strength, which can be analytically obtained by using the combinatorial matrix theory. Furthermore, we investigated the Kuramoto model and found an abnormal region ($C\leq 0.002$), in which the network has even worse synchronizability than the uncoupled case (C=0). On the other hand, the community effect will vanish when $C$ exceeds 0.1. Between these two extreme regions, a strong community structure will hinder global synchronization.

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