In this paper, we study stochastic impulsive reaction-diffusion neural networks with S-type distributed delays, aiming to obtain the sufficient conditions for global exponential stability. First, an impulsive inequality involving infinite delay is introduced and the asymptotic behaviour of its solution is investigated by the truncation method. Then, global exponential stability in the mean-square sense of the stochastic impulsive reaction-diffusion system is studied by constructing a simple Lyapunov-Krasovskii functional where the S-type distributed delay is handled by the impulsive inequality. Numerical examples are also given to verify the effectiveness of the proposed results. Finally, the obtained theoretical results are successfully applied to an image encryption scheme based on bit-level permutation and the stochastic neural networks.

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In this paper, a class of Nicholson-type delay systems with impulsive effects is considered. First, an equivalence relation between the solution (or positive periodic solution) of a Nicholson-type delay system with impulsive effects and that of the corresponding Nicholson-type delay system without impulsive effects is established. Then, by applying the cone fixed point theorem, some criteria are established for the existence and uniqueness of positive periodic solutions of the given systems. Finally, an example and its simulation are provided to illustrate the main results. Our results extend and improve greatly some earlier works reported in the literature.

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