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

• The key issues of the Markov property of mild solutions u t to the ISRDNNs with delays are discussed in the space of piecewise continuous functions (in general, u t is not a Markov process in R n). • The equivalent relation between the mild solutions to impulsive neural networks and those to the corresponding auxiliary systems is established. • The existence-uniqueness of mild solutions to ISRDNNs with delays is investigated, which generalized some of the results in the quoted literature. • Some easy-to-test algebraic criteria of the existence and exponential stability of mild periodic solutions to ISRDNNs with delays are given by virtue of the dissipative theory and the operator semigroup techniques. • The effectiveness of the proposed results is evidenced by illustrative simulations. 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. [ABSTRACT FROM AUTHOR]