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Chin. Phys. B, 2010, Vol. 19(2): 020501    DOI: 10.1088/1674-1056/19/2/020501
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Phase synchronization on small-world networks with community structure

Wang Xiao-Hua(王晓华)a)b), Jiao Li-Cheng(焦李成) a)†, and Wu Jian-She(吴建设)a)
a Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi'an 710071, China; b Aeronautical Computing Technique Research Institute, Xi'an 710068, China
Abstract  In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region (r ≤ 0.001), the network has even worse synchronizability than the case of isolated communities (r = 0). Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales: the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network.
Keywords:  complex networks      small-world      community structure      phase synchronization  
Received:  22 July 2009      Revised:  29 August 2009      Accepted manuscript online: 
PACS:  89.75.Hc (Networks and genealogical trees)  
  05.45.Xt (Synchronization; coupled oscillators)  
  87.23.Ge (Dynamics of social systems)  
Fund: Project supported in part by the National Natural Science Foundation of China (Grant Nos.~60673097, 60601029, 60672126 and 60702062), the National High-Tech Research and Development Plan of China (Grant Nos.~2009AA12Z210, 2008AA01Z125, 2007AA12Z136 and 2007AA12Z223), the National Research Foundation for the Doctoral Program of Higher Education of China (Grant Nos.~20060701007 and 20070701016), and Ministry & Commission-Level Research Foundation of China (Grant Nos.~XADZ2008159 and 51307040103).

Cite this article: 

Wang Xiao-Hua(王晓华), Jiao Li-Cheng(焦李成), and Wu Jian-She(吴建设) Phase synchronization on small-world networks with community structure 2010 Chin. Phys. B 19 020501

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