混合时滞随机Hopfield神经网络的均方渐近稳定性
Mean Square Asymptotic Stability of Stochastic Hopfield Neural Networks with Mixed Delays
摘要: 这篇文章考虑的是具有混合时滞的随机Hopfield神经网络模型，模型的混合时滞是由常固定时滞和连续分布时滞组成。李和丁(2017)引入了这种模型并且讨论了其性质，本文将继续对这种模型进行研究。因此，文章的主要目的是通过研究、分析来获得具有混合时滞的随机Hopfield神经网络的均方渐近稳定性的判定条件。除此之外，我们使用的方法是李雅普诺夫函数法、Ito公式法和不等式法。文章首先构造了合适的李雅普诺夫函数，然后对所构造的李雅普诺夫函数应用Ito公式，通过计算从而得到了判断具有混合时滞的随机Hopfield神经网络的均方渐近稳定性的条件。最后，我们给出了一个例子来验证我们所得到的结果。
Abstract: This paper considers a stochastic Hopfield neural network model with mixed delays, the mixed delays of the model are composed of constant fixed delay and continuously distributed delay. Li and Ding (2017) introduced this model and discussed its properties. In this paper, we will continue to study this model. Therefore, the main purpose of this paper is to obtain the criteria for the mean-square asymptotic stability of stochastic Hopfield neural networks with mixed delays through research and analysis. In addition, the methods we used are Lyapunov function method, Itô’s formula method and inequality method. First of all, we construct a suitable Lyapunov function. Then we apply Itô’s formula to the Lyapunov function. By calculation, we obtain the condition for judging the mean-square asymptotic stability of stochastic Hopfield neural networks with mixed delays. Lastly, we give an example to verify the results we obtained.
文章引用：谭亚华, 谭建国. 混合时滞随机Hopfield神经网络的均方渐近稳定性[J]. 动力系统与控制, 2019, 8(4): 263-270. https://doi.org/10.12677/DSC.2019.84028

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