Study On Two Classes Of Synchronization Of Complex Dynamical Networks

Complex networks are universal existent in the world. Many phenomena in nature can be described by complex networks, such as brain structures, protein interaction networks, science citation networks, food webs, social interactions, Internet, etc.. Synchronization is a typical behavior of complex dynamical networks, which has caused a lot of attention in recent decades. The synchronization control method of complex network is mainly divided into two categories: one is to improve the ability of the network by changing the properties of the network itself, such as changing the topology of the network, the coupling strength, etc.; the other is the control method to control theory research as a representative, which mainly includes variable control, pulse control, adaptive control, feedback control, driving-response synchronization, sliding mode control and so on.In this paper, we study the synchronization control of complex dynamical networks. Based on the adaptive method and Lyapunov stability theory, we study the synchronization control of complex dynamical networks. The main research work is summarized as follows:Firstly, an adaptive neural network matrix projective synchronization control method is designed for the unknown complex dynamic network with different node dimension. The information of the node itself and the neighbor nodes are also contained in the controller. The asymptotic convergence of the error and the boundedness of the parameter estimates are proved by Lyapunov stability analysis method. Finally, the effectiveness of the proposed method is verified by computer simulation.Secondly, the synchronization of complex dynamical networks with prescribed performance is studied and a distributed control law is designed for this network, which makes the error system asymptotically stable under the control law. Further, the error of the system is transformed to a coordinate transformation, the new error system is asymptotically stable under this control law, and meet prescribed performance and all the closed-loop signals are guaranteed. A numerical example is given to verify the validity of the proposed method.Finally, the synchronization of complex dynamical networks is summarized and prospect.