Exponential Stability And Existence Of Periodic Solution For Several Classes Of Neural Networks With Delays

In the past twenty years, many neural networks have been constructed by some researchers at home and abroad, for example, BAM neural networks, Hopfield neural networks. Cellular neural networks and so on. The stability of equilibrium and periodic solution for different classes of neural networks have been intensively studied and have been applied to engineering problems, physical problems and optimization problems. So. the neural networks have widely attracted more and more researchers. In this paper, we discuss the existence, uniqueness and global exponential stability of periodic solution and equilibrium for several classes of neural networks. This paper consists of four main parts as follows:In chapter 1, we simply introduce the background and significance of our investigation and main works of this paper.In chapter 2, By using the continuation theorem of coincidence degree theory, Lyapunov function and new inequality technique, the existence and global exponential stability of periodic solution are discussed for the delayed BAM neural networks with periodic coefficients. A new sufficient condition is obtained to ensure the existence and global exponential stability of periodic solution. Our existence criteria don't require that the activations functions satisfy differentiablety. boundness, monotous and the Lipschitz conditions. These results are more effective than previous works, which has an important leading significance in the designing globally exponentially stable of periodic solution for neural networks. These results extend and improve some previous works.In chapter 3, the Lozinskii measures of matrices and Schauder's fixed point theorem are employed to discuss the cellular neural network with distributed delays and varing coefficients. A new sufficient condition of the existence of periodic solution for cellular neural network is obtained.In chapter 4. the nonlinear measure approach and a novel Lyapunov function are employed to discuss the equilibrium of BAM neural networks. A better sufficient condition of the existence, uniqueness and global exponential stability of the equilibrium for BAM neural networks is obtained.