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

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.