S-分布时滞的随机Hopfield神经网络的稳定性

Stability of Stochastic Hopfield Neural Network with S-Type Distributed Delays

研究一类具有S-分布时滞的随机Hopfield神经网络的稳定性问题。通过构造随机Lyapunov泛函与随机分析技巧相结合的方法得到了实用有效的判别准则.具有S-分布时滞的Hopfield神经网络解决了具有离散时滞的Hopfield神经网络和具有连续分布时滞的Hopfield神经网络不能相互包含的问题。且本文在已有文献的系统模型中加入了随机干扰项,证明了该随机Hopfield神经网络全局解的存在唯一性及其全局均方鲁棒指数稳定性,使其具有更广泛的实际应用价值,推广了相关文献中的结果。

This paper is studied the stochastic Hopfield neural network with S-type distributed delays and investigated stability problems of this neural network.Some sufficient conditions on global robust exponential stability in mean square are established in this paper.The means are mainly constructing the suitable Lyapunov functional and applying the stochastic analysis techniques.Because the systems with discrete time delays and the systems with continuously distributed delays do not contain each other.However,S-distributed delays are introducted in stochastic neural network with time delays.It effectively solves the problem that discrete and distributed delays issues not included in the mutual.More even,the existence and uniqueness of solutions and the global robust exponential stability in mean square of the system are proved,which are promoted the results of the relevant literature.An example was given to show the correctnessof the conclusions.