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Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics |
Liu Zhao-Bing(刘兆冰), Zhang Hua-Guang(张化光)†, and Sun Qiu-Ye(孙秋野) |
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China |
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Abstract This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.
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Received: 27 January 2010
Revised: 15 April 2010
Accepted manuscript online:
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Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 60774048, and 60904101), and the Special Fund for Basic Scientific Research of Central Colleges, Northeastern University, China (Grant Nos. 090604005 and 090404009). |
Cite this article:
Liu Zhao-Bing(刘兆冰), Zhang Hua-Guang(张化光), and Sun Qiu-Ye(孙秋野) Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics 2010 Chin. Phys. B 19 090506
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[1] |
Watts D J and Strogatz S H 1998 Nature 393 440
|
[2] |
Barabási A L and Albert R 1999 Science 286 509
|
[3] |
Erdös P and R´enyi R 1959 Publications Mathematics 6 290
|
[4] |
Siljak D D 1991 Decentralized Control of Complex Sys-tems (New York: Academic Press)
|
[5] |
Dashkovskiy S, Ruffer B S and Wirth F R 2007 Mathe-matics Control, Signals and Systems 19 93
|
[6] |
Jiang Z P and Wang Y 2008 Proceeding of the 7th World Congress on Intelligent Control and Automation Chongqing, China, June 25-27, 2008 p1188-1193
|
[7] |
Li X,Wang X F and Chen G R 2004 IEEE Trans. Circuits Syst-I: Regular Papers 51 2074
|
[8] |
Chen T P, Liu X W and Lu W L 2007 IEEE Trans. Cir-cuits Syst-I: Regular Papers 54 1317
|
[9] |
Xiang J and Chen G R 2007 Automatica 43 1049
|
[10] |
Porfiri M and di Bernardo M 2008 Automatica 44 3100
|
[11] |
Zhou J, Lu J and Lü J H 2006 IEEE Trans. Automatic Control 51 652
|
[12] |
Zhou J, Lu J and Lü J H 2008 Automatica 44 996
|
[13] |
Yu W W, Chen G R and Lü J H 2009 Automatica 45 429
|
[14] |
Wu Y Y, Wei W, Li G Y and Xiang J 2009 IEEE Trans. Circuits Syst-II: Express Briefs 56 235
|
[15] |
Lu W L, Li X and Rong Z H 2010 Automatica 46 116
|
[16] |
Zou Y L and Chen G R 2009 Chin. Phys. B 18 3337
|
[17] |
Roy R, Murphy Jr T W, Maier T D and Gills Z 1992 Phys. Rev. Lett. 68 1259
|
[18] |
Hu G and Qu Z L 1994 Phys. Rev. Lett. 72 68
|
[19] |
Lü L and Zhang C 2009 Acta Phys. Sin. 58 1462 (in Chinese)
|
[20] |
Gao Y, Li L X, Peng H P, Yang Y X and Zhang X H 2008 Acta Phys. Sin. 57 1444 (in Chinese)
|
[21] |
Li J N and Zhang Q L 2009 Journal of Systems Engineer-ing and Electronics 19 1185
|
[22] |
Zhu J, Zhang Q L and Yang C Y 2009 Neurocomputing 72 2609
|
[23] |
Zhang H G, Xie Y H, Wang Z L and Zheng C D 2007 IEEE Trans. Neural Networks 18 1841
|
[24] |
Zhang H G, Huang W, Wang Z L and Chai T Y 2006 Phys. Lett. A 350 363
|
[25] |
Ma T D, Zhang H G and Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese)
|
[26] |
Zhang H G, Ma T D, Yu W and Fu J 2008 Chin. Phys. B 17 3616
|
[27] |
Ma T D, Zhang H G and Yu W 2008 Chin. Phys. B 17 4407
|
[28] |
Zhang H G, Wang Z L and Liu D R 2004 Int. J. Bifurca-tion and Chaos 14 3505
|
[29] |
Zhang H G, Wang Z L and Liu D R 2005 Int. J. Bifurca-tion and Chaos 15 2603
|
[30] |
Zhao Y, Zhang H G and Zheng C D 2008 Chin. Phys. B 17 529
|
[31] |
Zhang H G, Guan H X and Wang Z S 2007 Progress in Natural Science 17 687
|
[32] |
Zhang H G, Zhao Y, Yu W and Yang D S 2008 Chin. Phys. B 17 4056
|
[33] |
Zhang H G, Fu J, Ma T D and Tong S C 2009 Chin. Phys. B 18 969
|
[34] |
Zhang H G, Fu J, Ma T D and Tong S C 2009 Chin. Phys. B 18 3325
|
[35] |
Wang X Y and Wang Y 2008 Int. J. Mod. Phys. B 22 2453
|
[36] |
Wang X Y, Liu M, Wang M J and He Y J 2008 Int. J. Mod. Phys. B 22 2187
|
[37] |
Wang T S and Wang X Y 2009 Mod. Phys. Lett. B 23 2167
|
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