Mixed Delays And Neural Network Model Of The Equilibrium Point And The Existence Of Periodic Solutions And Exponential Stability

In this paper, the dynamic behaviors of solutions are considered for the discrete-time cellular neural network model with mixed delays and continuous-time Cohen-Grossberg neural network model with mixed delays. By using the continuation theorem of coincidence degree theory, Brouwer's fixed point theorem, Lyapunov functional method, matrix theory and inequality analysis technique, we study the existence and stability of periodic solution and equilibrium point for the above neural network model with mixed delays. The paper consists of four chapters.As the introduction, in Chapter 1, the background and history of artificial neural networks are briefly addressed. In Chapter 2, we discuss the existence and global exponential stability of equilibrium point for discrete-time cellular neural network with mixed delays and constant coefficients. In Chapter 3, we discuss the existence and global exponential stability of periodic solutions for discrete-time cellular neural network with mixed delays and variable coefficients. In Chapter 4, we discuss the existence of periodic solution for continuous-time Chen-Grossberg neural network with mixed delays, and a family of sufficient conditions is given for checking global exponential stability and the existence of periodic solutions of the neural network model.