Research On Synchronization Of Some Complex Dynamic Networks

A complex network is defined as a large set of coupled interconnected nodes by edges,in which a node is a fundamental unit having specific contents and exhibiting dynamical behavior,typicality.In recent years,with the further development of complex networks and the expansion of research field,it is more and more widely used.The synchronization phenomenon exists in all kinds of complex network systems,which is a typical collective behavior,and is one of the most important dynamic characteristics of complex networks.Therefore,it is of theoretical value and practical significance to study the synchronization of complex network systems.Among them,using synchronization of complex networks for secure communications has become one of hot spots of control science.This paper studies the function projective synchronization and the linear generalized synchronization of complex dynamic networks.And based on the Lyapunov stability theorem,the method of adaptive control has been employed to investigate the synchronization of some complex dynamical networks.Then,numerical examples as well as simulations are given to verify the feasibility of the proposed method.The main research work is summarized as follows:Firstly,the problems of projective synchronization of complex dynamical networks with time delay are studied.Based on the Lyapunov stability theorem,an appropriate adaptive controller,which can be used in practical production,is designed to realize the synchronization of complex dynamical networks with constant delay and time-varying delay.Secondly,based on the adaptive controller,the complex dynamical networks with time-varying coupling strength and time-varying coupling matrix are studied.By designing a controller,which a controller,the adaptive control laws and time-varying coupling strength or time-varying coupling matrix have a contact in the controller,this kind of networks achieve projective synchronization.Finally,the problem of linear generalized synchronization of a class of non-identical drive-response networks is studied.Based on the consideration of the time delay,the external disturbance and the uncertainty of inner coupling matrix in the response network,the sufficient condition for the linear generalized synchronization of the network system is obtained by designing a hybrid feedback controller.