School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China; Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom.
Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom.
Neural Netw. 2019 Aug;116:35-45. doi: 10.1016/j.neunet.2019.03.016. Epub 2019 Apr 4.
In this paper, we study stochastic impulsive reaction-diffusion neural networks with S-type distributed delays, aiming to obtain the sufficient conditions for global exponential stability. First, an impulsive inequality involving infinite delay is introduced and the asymptotic behaviour of its solution is investigated by the truncation method. Then, global exponential stability in the mean-square sense of the stochastic impulsive reaction-diffusion system is studied by constructing a simple Lyapunov-Krasovskii functional where the S-type distributed delay is handled by the impulsive inequality. Numerical examples are also given to verify the effectiveness of the proposed results. Finally, the obtained theoretical results are successfully applied to an image encryption scheme based on bit-level permutation and the stochastic neural networks.
本文研究了具有 S 型分布时滞的随机脉冲反应扩散神经网络，旨在获得全局指数稳定性的充分条件。首先，引入了一个包含无穷时滞的脉冲不等式，并通过截断法研究了其解的渐近行为。然后，通过构造一个简单的 Lyapunov-Krasovskii 泛函，研究了随机脉冲反应扩散系统在均方意义下的全局指数稳定性，其中 S 型分布时滞由脉冲不等式处理。还给出了数值示例来验证所提出结果的有效性。最后，将所得到的理论结果成功应用于基于位级排列和随机神经网络的图像加密方案。
