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

作　　者：刘兆冰 张化光 孙秋野 

机构地区：[1]College of Information Science and Engineering,Northeastern University

出　　处：《Chinese Physics B》2010年第9期250-260,共11页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.50977008,60774048,and 60904101);the Special Fund for Basic Scientific Research of Central Colleges,Northeastern University,China(Grant Nos.090604005 and090404009)

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.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.

关 键 词：uncertain complex network pinning control synchronisation adaptive tuning 

分 类 号：O157.5[理学—数学] O231[理学—基础数学]