Exponential Stability Of Periodic Solutions In Fuzzy Neural Networks

The research of neural networks was started since 40's last century. For neural networks, it is applied in many different areas,such as pattern recognition, associative memory and combinatorial optimization. Nowadays,many neural networks have been constructed by some mathematicians all over the world. For example,Hopfield neural networks,BAM neural networks, Cellular neural networks and so on. Because of its wide application, more and more mathematicians become interested in the study of dynamical behaviors of neural networks.In practice uncertainty or vagueness is often encountered. In 1996, Tao Yang and Lin Bao Yang introduce fuzzy theory into neural networks.Based on traditional cellular neural networks,fuzzy cellular neural network was proposed. Time delays are unavoidable in the life, and we can't take no notice of it. So it's very important to consider the fuzzy neural networks with delays in both theory and practice. In this thesis, by using Lyapunov function method,M-matrix theory and linear matrix inequality,we describe some important properties of dynamic behaviors of two kinds of fuzzy neural networks, which includes the existence,uniqueness and exponential stability of the periodic solutions.The paper is composed of four chapters.Chapter 1,we introduce the background of neural networks and the recent development. In Chapter 2, the main purpose is to study of a class of fuzzy Hopfield neural networks (FHNN) with distributed delays.By using the stability of Lyapunov function, sufficient condition for the global exponential stability and existence of periodic solutions.Finally, an example is given to show the effectiveness of our results.In Chapter 3,a class of fuzzy Hopfield neural networks (FHNN)with distributed delays is considered. A sufficient condition for the existence periodic solutions and global exponential stability is obtained by using linear matrix inequality (LMI) and the Lyapunov-Krasovskill functional.The results of this paper are new. An illustrative example is given to demonstrate the effectiveness of the obtained results.In Chapter 4, by establishing an integro-differential inequality, a class of fuzzy cellular neural networks with mixed delays is investigated.