Practical Exponential Stability of Impulsive Stochastic Reaction-Diffusion Systems With Delays

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 pth 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.

Automated summary

This article studies the practical exponential stability of impulsive stochastic reaction-diffusion systems (ISRDSs) with delays. The direct approach and the Lyapunov method are developed to investigate the stability and convergence rate. The practical stability results are successfully applied to the impulsive reaction-diffusion stochastic Hopfield neural networks (IRDSHNNs) with delays.