Periodic solutions to stochastic reaction-diffusion neural networks with S-type distributed delays

In this paper, the existence and stability of mild periodic solutions to the stochastic reaction–diffusion neural networks (SRDNNs) with S-type distributed delays are studied. First, the key issues of the Markov property of mild solutions to the SRDNNs with S-type distributed delays in $C^{b}$ -space are investigated. Next, the existence of mild periodic solutions is discussed by the dissipative theory and the operator semigroup theory. Then, some sufficient conditions ensuring the stability of mild periodic solutions are derived by the Lyapunov method. To overcome the difficulties created by the special features possessed by S-type distributed delays, the truncation method is applied. Finally, a numerical example is given to illustrate the feasibility of our results.