Phase synchronization on small-world networks with community structure

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

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20501-020501.doi: 10.1088/1674-1056/19/2/020501

Phase synchronization on small-world networks with community structure

焦李成¹, 吴建设¹, 王晓华²

(1)Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi'an 710071, China; (2)Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi'an 710071, China %\vglue-6pt \address{b){Aeronautical Computing Technique Research Institute, Xi'an 710068, China

收稿日期:2009-07-22 修回日期:2009-08-29 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
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).

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

Received:2009-07-22 Revised:2009-08-29 Online:2010-02-15 Published:2010-02-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: complex networks, small-world, community structure, phase synchronization

中图分类号: (Networks and genealogical trees)

89.75.Hc

05.45.Xt (Synchronization; coupled oscillators) 87.23.Ge (Dynamics of social systems)

王晓华, 焦李成, 吴建设. Phase synchronization on small-world networks with community structure[J]. 中国物理B, 2010, 19(2): 20501-020501.

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[J]. Chin. Phys. B, 2010, 19(2): 20501-020501.

参考文献 32

[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

Phase synchronization on small-world networks with community structure

Phase synchronization on small-world networks with community structure

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Fuzhong Nian(年福忠) and Xia Zhang(张霞). Topological phase transition in network spreading[J]. 中国物理B, 2023, 32(3): 38901-038901.
[2]	Dan-Dan Zhao(赵丹丹), Wang-Xin Peng(彭王鑫), Hao Peng(彭浩), and Wei Wang(王伟). Effects of heterogeneous adoption thresholds on contact-limited social contagions[J]. 中国物理B, 2022, 31(6): 68906-068906.
[3]	Yijun Ran(冉义军), Tianyu Liu(刘天宇), Tao Jia(贾韬), and Xiao-Ke Xu(许小可). A novel similarity measure for mining missing links in long-path networks[J]. 中国物理B, 2022, 31(6): 68902-068902.
[4]	Dong-Jie Qian(钱冬杰). Explosive synchronization in a mobile network in the presence of a positive feedback mechanism[J]. 中国物理B, 2022, 31(1): 10503-010503.
[5]	Yu-Wei Yan(严玉为), Yuan Jiang(蒋沅), Rong-Bin Yu(余荣斌), Song-Qing Yang(杨松青), and Cheng Hong(洪成). Cascading failures of overload behaviors using a new coupled network model between edges[J]. 中国物理B, 2022, 31(1): 18901-018901.
[6]	Fuzhong Nian(年福忠), Jingzhou Li(李经洲), and Xin Guo(郭鑫). Evolution mechanism of Weibo top news competition[J]. 中国物理B, 2021, 30(12): 128901-128901.
[7]	Dongli Duan(段东立), Tao Chai(柴涛), Xixi Wu(武茜茜), Chengxing Wu(吴成星), Shubin Si(司书宾), and Genqing Bian(边根庆). Identification of unstable individuals in dynamic networks[J]. 中国物理B, 2021, 30(9): 90501-090501.
[8]	Tong-Feng Weng(翁同峰), Xin-Xin Cao(曹欣欣), and Hui-Jie Yang(杨会杰). Complex network perspective on modelling chaotic systems via machine learning[J]. 中国物理B, 2021, 30(6): 60506-060506.
[9]	Zi-Wei Yuan(袁紫薇), Chang-Chun Lv(吕长春), Shu-Bin Si(司书宾), and Dong-Li Duan(段东立). Dynamical robustness of networks based on betweenness against multi-node attack[J]. 中国物理B, 2021, 30(5): 50501-050501.
[10]	Xiao-Long Peng(彭小龙) and Yi-Dan Zhang(张译丹). Contagion dynamics on adaptive multiplex networks with awareness-dependent rewiring[J]. 中国物理B, 2021, 30(5): 58901-058901.
[11]	. [J]. 中国物理B, 2021, 30(4): 48901-.
[12]	. [J]. 中国物理B, 2020, 29(12): 128901-.
[13]	. [J]. 中国物理B, 2020, 29(12): 128902-.
[14]	苏桂锋, 李晓温, 张小兵, 张一. Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks[J]. 中国物理B, 2020, 29(8): 88904-088904.
[15]	闫小丽, 崔亚鹏, 倪顺江. Identifying influential spreaders in complex networks based on entropy weight method and gravity law[J]. 中国物理B, 2020, 29(4): 48902-048902.