具分布参数的随机Hopfield神经网络的指数稳定(英文)

Exponential stability of stochastic Hopfield neuralnetworks with distributed parameters

基于随机Fubini定理,将随机偏微分方程描述的Hopfield神经网络系统转化为用相应的随机常微分方程来描述.利用关于空间变量平均的Lyapunov函数与It^o公式,通过对所构造的Lyapunov函数在It^o微分规则下对相应系统求导的方法,获得了系统指数稳定的代数判据及其Lyapunov指数估计.实现了运用Lyapunov直接法对分布参数系统稳定性的研究.

Based on stochastic Fubini theorem,the Hopfield neural network system depicted by a stochastic partial differential equation is translated into a stochastic ordinary differential equation.By constructing a mean Lyapunov function with respect to (the space) variables and using It formula under the integral operators,the exponential stability of stochastic neutral systems with (distributed parameters) is investigated by deviating of the function along the trajectories of the systems.Also,the Lyapunov exponent estimate is obtained.Thus,the stability of stochastic systems with distributed parameters is studied by Lyapunov direct method.