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In this article, a novel semi-discrete model for stochastic competitive neural networks (SCNNs) is proposed. At first, taking advantage of some famous inequalities and fixed point theory, a few conditions are obtained for the existence of 2p-th mean almost periodic sequence (MAPS) of the semi-discrete stochastic model. In the next palace, 2p-th moment global exponential stability (MGES) of the above model is discussed as well. The research findings exhibit the stochastic and delayed effects on the mean dynamics of the semi-discrete stochastic networks. In the end, some numerical illustrations are presented to visually expound the feasibility of the works in this paper. The methods in this article could be applied to investigate other models in the areas of science and engineering.