The Research On The Dissipative And The Chaotic Synchronization Of The Neural Network

Because there is information delay between neurons in the process of exchanging information and signal transmission,the time delay will lead to the change of the performance of the network system,which makes the stable system unstable.Therefore,the study of differential equations with delay has important theoretical significance and practical application value.In this paper,we study the global dissipative problem of a class of BAM neural networks with mixed delays and the synchronization of complex networks in finite time by using the theory and method of functional differential equations.The main work of this paper is as follows:Firstly,using the theory of functional differential equation,by constructing Lyapunov functional,the problem of dissipative BAM neural networks with mixed delays,by using the linear matrix inequality approach is given for BAM neural networks with mixed delays is a new criterion of global dissipation.The effectiveness of the obtained results is verified by numerical simulation.Secondly,The finite time chaotic synchronization coupling network is studied.Because of the time lag between the states of each node,the internal delay and the coupling delay vary with time.In this paper,we study the finite time synchronization of two coupled networks in general,and not only consider the difference of the internal delay and the coupling delay,but also the study of the coupling system with a single time varying delay.Based on the Lyapunov stability theory,a feedback controller is designed to realize the synchronization of two time varying delay coupled networks in finite time.