Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

doi:10.1088/1674-1056/19/9/090506

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90506-090506.doi: 10.1088/1674-1056/19/9/090506

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

刘兆冰, 张化光, 孙秋野

College of Information Science and Engineering, Northeastern University, Shenyang 110819, China

收稿日期:2010-01-27 修回日期:2010-04-15 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
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

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

Received:2010-01-27 Revised:2010-04-15 Online:2010-09-15 Published:2010-09-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: uncertain complex network, pinning control, synchronisation, adaptive tuning

中图分类号:

0545

刘兆冰, 张化光, 孙秋野. Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics[J]. 中国物理B, 2010, 19(9): 90506-090506.

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[J]. Chin. Phys. B, 2010, 19(9): 90506-090506.

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Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

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