Finite-time Synchronization And Finite-time Anti-synchronization Analysis Of Neural Networks

Synchronization and anti-synchronization are important dynamic behaviors in neural network,different neural network models can achieve different types of synchronization and anti-synchronization under the function of reasonable controller.In this paper,we study the finite-time synchronization problem of a class of complex valued BAM neural networks with time-delay,and the finite-time anti-synchronization problem of a class of neural networks with time-varying delay.Without using the LMI method and the finite-time stability theorem,by constructing Lyapunov function,four differential inequalities are obtained by using the method of enlarging and reducing,and then by using the techniques of the method of gather together differentiation and integral transformation,two new sufficient conditions are proposed to ensure the finitetime synchronization of the complex valued BAM neural network with time delay.In addition,by combining the integral inequality technique with other inequality techniques,a first-order differential inequality is constructed to solve the problem,and two new sufficient conditions are obtained to guarantee the finite-time anti-synchronization of the time-varying delay neural network in question.Compared with the existing results,the results obtained in this paper are more universal and expand the previous work.The paper is divided into four chapters,the main contents are as follows:In chapter 1,we introduce the background,significance,related preparatory knowledge,research status,innovation and main work of the complex valued BAM neural network and time-varying delay neural network.In chapter 2,sufficient conditions for finite-time synchronization between driving system and response system of BAM neural network with complex delay are studied,and the effectiveness of the conditions obtained in the theorem is illustrated by numerical examples.In chapter 3,the sufficient conditions for finite-time anti-synchronization between the time-varying delay neural network drive system and the response system are studied,and the validity of the conditions in the theorem is illustrated by numerical examples.Finally,the main work of this paper is summarized and the main direction of future work is pointed out.