IEEE Trans Cybern. 2022 May;52(5):2687-2697. doi: 10.1109/TCYB.2020.3022024. Epub 2022 May 19.
This article studies the practical exponential stability of impulsive stochastic reaction-diffusion systems (ISRDSs) with delays. First, a direct approach and the Lyapunov method are developed to investigate the p th moment practical exponential stability and estimate the convergence rate. Note that these two methods can also be used to discuss the exponential stability of systems in certain conditions. Then, the practical stability results are successfully applied to the impulsive reaction-diffusion stochastic Hopfield neural networks (IRDSHNNs) with delays. By the illustration of four numerical examples and their simulations, our results in this article are proven to be effective in dealing with the problem of practical exponential stability of ISRDSs with delays, and may be regarded as stabilization results.
本文研究了时滞脉冲随机反应扩散系统（ISRDSs）的实用指数稳定性。首先，采用直接法和 Lyapunov 方法研究了 p 阶矩实用指数稳定性，并估计了收敛速度。值得注意的是，这两种方法也可用于在某些条件下讨论系统的指数稳定性。然后，实用稳定性结果成功应用于时滞脉冲随机反应扩散 Hopfield 神经网络（IRDSHNNs）。通过四个数值例子及其仿真，证明了本文的结果在处理时滞脉冲随机反应扩散系统的实用指数稳定性问题方面是有效的，可以看作是镇定结果。
