Periodic solutions to impulsive stochastic reaction-diffusion neural networks with delays

In this paper, the aims are to study the existence and stability of mild periodic solutions to impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with delays. First, key issues of the Markov property of mild solutions to ISRDNNs with delays are presented in the space of piecewise continuous functions. Next, combining the operator semigroup method with other mathematical techniques, the existence of mild periodic solutions is proposed and some relevant results are generalized. Then, the exponential stability of mild periodic solutions is discussed and some easy-to-test sufficient conditions are obtained by using the Lyapunov method. Finally, numerical simulations are provided to illustrate the effectiveness of our results. (C) 2019 Elsevier B.V. All rights reserved.