The Stability Of Several Types Of Random Neural Network Analysis

In accordance with the views of neurophysiology, biological neurons are essentially random, because the neural network repeatedly received the same stimulus, its response is not the same, which means that the randomness in biological neural networks play an important role. Therefore, studying the stability of stochastic neural networks has been a hotspot issue and achieved many important results. In the other hand, artificial neural networks are basically simulated by electronic circuits, electronic switches, capacitors must be reflected by the delays. Therefore, studying the impact of delays on neural networks is very necessary. However, the results on stability of time-delay neural networks, are mostly studied on the constant delays, in particular, research on stability of stochastic fuzzy cellular neural networks with time-varying delays and stochastic Cohen-Grossberg neural networks of neutral type have not be seen up to now. This paper aims at the stabilitys of the above-mentioned models. The paper is composed of four parts.In Chapter 1, we first reviewed the history of neural networks and stochastic neural networks. Then, some common applications of neural network model are described. Finally, we briefly describe the significance, methods and results of our studies.In Chapter 2, by using the Razumikhin-type theorem and the Lyapunov functional method, the mean square exponential stability of stochastic fuzzy cellular neural networks with time-varying delays is studied. Some examples are given to illustrate the theoretical results in this chapter.In Chapter 3, by using the Lyapunov functional method and the semi-martingale convergence theorem, the almost surely exponential stability of the stochastic fuzzy cellular neural network with mixed delays is presented. At last, some examples are presented.In Chapter 4, by using the linear matrix inequality (LMI) theory and the Lyapunov functional method, the global asymptotic stability for stochastic Cohen-Grossberg neural networks of neutral type is studied. At last, some examples are given.