Stability Analysis For Two Classes Of Hopfield Neural Networks

In recent years, the Hopfield neural network has been widely studied, and has already been successfully applied to signal processing,pattern recognition,combination optimization and so on. Because the Hopfield neural network with time delays has important application in solving the problem of dynamic image processing Therefore, A study on Hopfield neural network with time delays has been paid close attention by many scholars.Stability is a key issue in applications of neural networks.In some applications, it is desirable that the network possesses a unique and globally asymptotically stable equilibrium point for every external input. In researching this thesis, we choose a Lyapunov function to suit neural networks, through in theory of stability and neural networks, and then dispose the matrix with some skills. We get a better liner matrix inequality result, including global asymptotically stability and global exponential stability of time delays neural network. In these years, stability analysis of neural network turns to be hotspot, but most of existing results derived in the literature are independent of the delay parameters, how to propose a delay-dependent stability criterion for delayed cellular neural networks is a hot problem. In this thesis we present delay-dependent stability criterion, so as to get the maximum numerical delay and some results independent of the delay parameters easily. And more, stability analysis of a second order neural network of Hopfield in this paper is a new task, which is an experiment in stability analysis of high order neural network. At last, we present numerical examples to illustrate the validity of the results.