|
|
Pinning control of complex networks via network division |
WU Ying-ying, WEI Wei, LI Guo-yang |
Department of System Science and Engineering, Zhejiang University, Hangzhou 310027, China |
|
|
Abstract Based on V-stability theory, a novel pinning control strategy for the stability problem of complex large scale network was presented via studying the relationship between the original network and its communities. In the case of certain criterions, the network was separated into small communities by a fast division algorithm before applying pinning control for deriving stabilization. The new control method which needs less number of pinned nodes is more effective and practical than the previous specifically pinning strategy. As illustrative examples, several network models were simulated to verify the results.
|
Published: 16 March 2012
|
|
基于社团划分的复杂网络牵制控制策略
为了解决大尺度复杂网络的稳定性问题,通过研究原网络稳定性与其子群落稳定性之间的关系,在V稳定性理论的基础上,提出一种新的牵制控制策略.在满足一定衡量标准的情况下,对原网络先应用快速分群法,将其划分成几个独立的子群落,再依次对每个子群落进行特定牵制控制的策略能够实现复杂网络的V稳定.研究结果表明:这种控制策略与直接对原网络进行特定牵制控制相比,所需控制器的个数更少,控制方法的实用性和有效性都得到了提高.
|
|
[1] WANG X F, CHEN G. Pinning control of scalefree dynamical networks [J]. Physica A: Statistical Mechanics and its Applications, 2002, 310(3/4): 521-531.
[2] WANG Y W, WEN C Y. A survey on pinning control of complex dynamical networks [C]∥2008 10th International Conference on Control Automation Robotics & Vision. Hanoi: [s. n.], 2008: 64-67.
[3] ZHOU J, LU J A, LU J H. Pinning adaptive synchronization of a general complex dynamical network [J]. Automatica, 2008, 44(2): 996-1003.
[4] PORFIRI M, FIORILLI F. Nodetonode pinning control of complex networks [J]. Chaos, 2009, 19(1): 013122.
[5] CHEN T, LIU X, LU W. Pinning complex networks by a single controller [J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2007, 54(6): 1317-1326.
[6] XIANG J, CHEN G R. On the Vstability of complex dynamical networks [J]. Automatica, 2007, 43(6): 1049-1057.
[7] WU Y Y, WEI W, LI G Y, et al. Pinning control of uncertain complex networks to a homogeneous orbit [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2009, 56(3): 235-239.
[8] GIBSON D, KLEINBERG J. RAGHAVAN P. Inferring Web communities from link topology [C]∥ Proceedings of the 9th ACM Conference on Hypertext and Hypermedia: Links, Objects, Time and Spacestructure in Hypermedia Systems. Pittsburgh:\ [s.n.\], 1998: 225-234.
[9] FLAKE G W, LAWRENCE S, GILES C L, et al. Selforganization and identification of Web communities [J]. Computer, 2002, 35(3): 66-70.
[10] ADAMIC L A, ADAR E. Friends and neighbors on the Web [J]. Social Networks, 2003, 25(3): 211-230.
[11] GIRVAN M, NEWMAN M E J. Community structure in social and biological networks [J]. Proceedings of the National Academy of Sciences of the United States of America, 2002, 99(12): 7821-7826.
[12] ZACHARY W W. An information flow model for conflict and fission in small groups [J]. Journal of Anthropological Research, 1977, 33: 452-473.
[13] 汪小帆, 李翔, 陈关荣. 复杂网络理论及其应用 [M]. 北京: 清华大学出版社, 2006: 162-193.
[14] NEWMAN M E J, GIRVAN M. Finding and evaluating community structure in networks [J]. Physical Review E, 2004, 69(2): 026113.
[15] LI R, DUAN Z S, CHEN G R. Cost and effect of pinning control for network synchronization [J]. Chinese Physics B, 2009, 18(1): 106-118.
[16] WU W, ZHOU W, CHEN T. Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control [J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2009, 56(4): 829-839.
[17] WU Y Y, WEI W, XIANG J. Pinning control on complex networks via identifying communities [C]∥2009 Chinese Control and Decision Conference. Guilin: IEEE Computer Society, 2009: 1077-1081.
[18] NEWMAN M E J. Fast algorithm for detecting community structure in networks [J]. Physical Review E, 2004, 69(6): 066133(5).
[19] ERDS P, RNYI A. On the evolution of random graphs [J]. Bulletin de I’Institut Intemaxioral de Statistique,1961,38(4): 143-347.
[20] WATTS D J, STROGATZ S H. Collective dynamics of 'smallworld networks [J]. Nature, 1998, 393(6684): 440-442.
[21] BARABSI AL, AlBERT R. Emergence of scaling in random networks [J]. Science, 1999, 286(5439): 509-512.
[22] LI C G, MAINI P K. An evolving network model with community structure [J]. Journal of Physics aMathematical and General, 2005, 38(45): 9741-9749. |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|