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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 the random Fubini theorem, the Hopfield neural network system described by stochastic partial differential equations is transformed into the corresponding stochastic ordinary differential equations to describe. Using the Lyapunov function and It ^ o formula which averages the spatial variables, the Lyapunov function It ^ o differential rules under the guidance of the corresponding system, access to the system exponential stability of the algebraic criteria and its Lyapunov exponent estimation achieved using Lyapunov direct method of distribution parameter system stability.