随机Hopfield神经网络渐进行为的变互式凸组合方法

Reciprocally Convex Approach to Asymptotic Behavior of Stochastic Hopfield Neural Networks

摘要: 本文通过构造合适Lyapunov-Krasovskii泛函，采用变互式凸组合方法、自由权矩阵方法、随机分析技巧、线性矩阵不等式(LMI)方法，研究了一类随机Hopfield神经网络的随机一致最终有界性、随机吸引子的存在性以及均方指数的稳定性。我们得到了随机Hopfield神经网络的新的结果和时滞依靠的充分条件。最后，应用MATLAB数值模拟检验来得到了理论的有效性。

Abstract: In this paper, the problems of stochastic uniformly ultimate boundedness, the existence of stochastic attractor and mean square exponential stability for stochastic Hopfield neural networks are studied by constructing proper Lyapunov-Krasovskii functional, utilizing the reciprocally con- vex approach, the free-weighting matrix method, some stochastic analysis techniques and linear matrix inequalities technique (LMI). We deduce novel results and delay-dependent sufficient conditions for stochastic Hopfield neural networks. Finally, numerical simulations are given on MATLAB to verify the effectiveness of the gained results.