随机时滞Hopfield神经网络的均方指数稳定性

The Mean Square Exponential Stability of a Hopfield Type Stochastic Neural Network with Time Delay

利用Ｌｙａｐｕｎｏｖ泛函和Ｉｔｏ公式，研究了具有时滞的随机Ｈｏｐｆｉｅｌｄ型神经网络的均方指数稳定性．证明了三条定理和三个推论．当随机扰动为零时，便得到确定性的时滞神经网络指数稳定的结果．

In this paper we shall investigate the mean square exponential stability for a Hopfield type stochastic neural network with time delay. By the Lyapunov functional and It formula, three theorems and three collaries are proved. In each theorem, the second order moment Lyapunov exponent of the solution for the stochastic network is given. When stochastic perturbation σ(x, y)≡0 , the network becomes a deterministic one with time delay. As corollaries, some useful criteria for the delay network to be exponentially stable are obtained and these corollaries are new even to the exponential stability of ordinary differential equations with time delay.