In this thesis,we consider the following discrete BAM(Bidirectional Associative Memories)neural network system with time-varying input(?)(1.1)and discuss its boundness,nonoscillation and asymptotic behavior.The thesis includes three chapters,and the summary for each chapter is as follows:The first chapter is the preliminaries of this thesis.We first introduce the position of neural networks in the field of artificial intelligence and several important mathematical models of neural networks.Then,we describe briefly the application background and research status of time-delay neural networks,and give our motivation for studying the present subject.In the second chapter,we investigate the bounded and nonoscillatory properties of the system(1.1).To begin with,we give two criteria to guarantee the system(1.1)is bounded by using the matrix inequality properties,mathematical induction,Lyapunov function method and limit theory.Then,we discuss the sufficient conditions for the system(1.1)being nonoscillatory.Here the nonoscillation includes the nonoscillation of the solutions of system(1.1),and the nonoscillation between the solutions of system(1.1)and the equilibrium solution corresponding to the constant input system.Besides,some examples are provided to illustrate our main results.The third chapter is devoted to studying the asymptotic behavior of the system(1.1).In this chapter,by constructing an appropriate Lyapunov function,a sufficient criterion is obtained,which ensures any two solutions of the system(1.1)are asymptotic.Then,by using the mathematical induction,another asymptotical condition is derived,which makes any two solutions of system(1.1)being globally exponentially asymptotically near.Similar constructing and analyzing methods are also used to derive two sufficient criteria which make any solution of system(1.1)being asymptotically near to the equilibrium solution corresponding to the constant input system.Finally,an example is provided to verify our obtained conclusions. |