一类具有时滞脉冲的反应扩散神经网络的指数稳定性

Exponential Stability of a Class of Reaction-diffusion Neural Networks with Delayed Impulses

反应扩散方程模型被广泛应用于描述各类动力系统。本文研究了一类具有反应扩散项、可变时滞、连续时滞脉冲的神经网络的全局指数稳定性问题。首先构造Lyapunov函数,然后利用狄利克雷边界条件对反应扩散项进行运算得到时滞脉冲不等式,结合常数变易公式,推导出了带有脉冲时滞反应扩散方程的平衡点的全局指数稳定的充分条件,最后通过一个实例对得到的结果进行了具体应用。该结果推广并改进了带有可变时滞的反应扩散神经网络系统的相关结果。

Reaction diffusion equation models are widely used to describe various dynamical systems.In this paper,the global exponential stability of a class of neural networks with reaction-diffusion term,variable delay and continuous delay impulses is studied.Firstly,the Lyapunov function is constructed,and then the delay impulsive inequality is obtained by using the Dirichlet boundary condition to operate the reaction-diffusion term.Combined with the constant variation formula,the sufficient conditions for the global exponential stability of the trivial solution of the reaction-diffusion equation with impulsive delay are derived.Finally,an example is given to demonstrate the application.This result generalizes and improves the relevant results of reaction-diffusion neural network systems with variable delay.