Phase synchronization on small-world networks with community structure

doi:10.1088/1674-1056/19/2/020501

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

[1]	Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47
[2]	Newman M E J 2003 SIAM Rev. 45 167
[3]	Watts D J and Strogatz S H 1998 Nature 39 3 440
[4]	Barabási A L and Albert R 1999 Science 286 509
[5]	Girvan M and Newman M E J 2002 Proc. Nat. Acad. Sci.USA 99 7821
[6]	Du H F, Li S Z, Marcus W F, Yue Z S and Yang X S 2007 Acta Phys. Sin. 56 6886 (in Chinese)
[7]	Palla G, Derényi I, Farkas I and Vicsek T 2005 Nature 435 814
[8]	Eriksen K A, Simonsen I, Maslov S and Sneppen K 2003 Phys. Rev. Lett. 90 148701
[9]	Arenas A, Danon L, Diaz-Guilera A, Gleiser P M and Guimerà R 2004 Eur. Phys. J. B 38 373
[10]	Krause A E, Frank K A, Mason D M, Ulanowicz R E and Taylor W W 2003 Nature 426 282
[11]	Liu Y K, Li Z, Chen X J and Wang L 2009 Chin. Phys. B 18 2623
[12]	Cui D, Gao Z Y and Zhao X M 2008 Chin. Phys.B { 17 1703
[13]	Zhang Z, Fu Z Q and Yan G 2009 Chin. Phys. B 18 2209
[14]	Cui D, Gao Z Y and Zheng J F 2009 Chin. Phys. B 18 516
[15]	Wang X H, Jiao L C and Wu J S 2009 Physica A DOI: 10.1016/j.physa.2009.08.032
[16]	Newman M E J and Watts D J 1999 Phys. Lett. A 26 3 341
[17]	Kleinberg J 2000 Nature 406 845
[18]	Pan R K and Sinha S 2009 Europhys. Lett. 85 68006
[19]	Kanovsky I 2006 Complex Networks Clustering and Edges Correlation, NetSci 2006(Indiana: Bloomington USA)
[20]	Huang L, Park K, Lai Y C, Yang L and Yang K 2006 Phys. Rev. Lett. 97 164101
[21]	Atay F M, Biyikoglu T and Jost J 2006 IEEE Trans. Circuits and Systems 5 3 92
[22]	Arenas A, Diaz-Guilera A, Kurths J, Moreno Y and Zhou C 2008 Phys. Rep. 46993
[23]	Arenas A, Diaz-Guilera A and Perez-Vicente C J 2006 Phys. Rev. Lett. 96 114102
[24]	Wang X H, Jiao L C and Wu J S 2009 Physica A 388 2975
[25]	Moreno Y, Vazquez-Prada M and Pacheco A F 2004 Physica A 34 3 279
[26]	Oh E, Rho K, Hong H and Kahng B 2005 Phys. Rev.E 72 047101
[27]	Feng C F, Xu X J, Wu Z X and Wang Y H 2008 Chin. Phys. B 17 1951
[28]	Zhou T, Zhao M, Chen G R, Yan G and Wang B H 2007 Phys. Lett.A 368 431
[29]	Kuramoto Y 1984 Chemical Oscillations, Wave and Turbulence (Berlin: Springer-Verlag)
[30]	Latora V and Marchiori M 2001 Phys. Rev. Lett. 87 198701
[31]	Newman M E J and Girvan M 2004 Phys. Rev.E 69 026113
[32]	Boccaletti S, Ivanchenko M, Latora V, Pluchino A and Rapisarda A 2007 Phys. Rev. E 75 045102

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