On The Dynamical Behaviors In Nonautonomous Delayed Neural Networks

An in-depth research on the dynamical behaviors in nonautonomous delayed neural networks is made in this thesis. Our main purpose is to establish the criteria on the boundedness. global asymptotic stability and global exponential stability of the solution, and the existence, uniqueness of periodic solution and almost periodic solution and its global stability for nonautonomous neural networks with delays. The stability theory of general functional differential equations, Liapunov functional method, the theorem of boundedness of solution, the continuation theorem based on coincidence degree theory, matrix theory, the theory of periodic solution and almost periodic solution and the theory of general functional differential equations with infinite delay are extensively applied in this thesis.At first, the theme, aim and meaning of the research are clarified. A survey is presented on dynamical behavior of neural networks, as well as the methods of research. The contents of the future research are proposed.In Chapter 2, we study the dynamical behaviors of neural networks with multiple time-varying delays. Our main purpose is to establish the criteria of matric form, we first study autonomous cellular neural networks with multiple time-varying delays. By constructing suitable Liapunov functional, utilizing the technique of matrix analysis, we obtain the sufficient criteria of matrix form on the existence, uniqueness and global exponential stability of equilibrium point. Secondly, we discuss nonautonomous neural networks with bounded delay. By using Liapunov functional method and the matrix analysis technique, we obtain the sufficient conditions on the boundedness, global exponential stability and the existence, uniqueness and its global exponential stability.Comparing with results of previous literature, the results obtained in this chapter improve and extend results of previous literature in many respects.In Chapter 3, we study nonautonomous bounded delayed neural networks. Our main purpose is to establish the diagonal dominant form criteria. By introducing ingeniously many real parameter, applying the technique of Young inequality and the essential theorem for general functional differential equations, we obtain the sufficient conditions on the boundedness, global exponential stability, the existence of periodic solution and its global exponential stability for nonautonomous delayed neural networks, nonautonomous delayed BAM neural networks and nonautonomous delayed recurrent neural networks. As a special case of nonautonomous neural networks, when the systems degenerate into autonomous systems, we obtain the existence, uniqueness and global exponential stability of equilibrium point. The results given in this chapter are significant and useful in theory and application.In Chapter 4, we discuss the boundedness and stability of solutions and the existence of periodic for nonautonomous neural networks with infinite delay. We see that the existence of periodic solution for nonautonomous neural networks with infinite delay is a complex problem. In order to obtain the existence of periodic solution, by introducing the Banach space Cg(R-) and constructing suitable Liapunov functional, applying the essential theorem for general functional differential equations with infinite and the technique of Young inequality, we establish a series of criteria on the boundedness, global stability, the existence of periodic and its global stability. In these criteria, we do not require that the activation functions are differentiable, bounded and monotone nondecreasing. Some previous works are improved and extended.In Chapter 5, we first study the existence of periodic solution by using the continuation theorem based on coincidence degree theory and Liapunov function method, sufficient and realizable conditions are obtained on the existence of periodic solution for neural networks with variable coefficients and time-varying delays.Secondly, we study the existence, uniqueness od almost periodic solution and its global exponential...