Fixed-Time Stabilization of Reaction-Diffusion Memristive Neural Networks Under Multiple Stochastic Noise and Deception Attacks

This paper investigates the fixed-time mean-square exponential stabilization problem of reaction-diffusion memristive neural networks (RDMNNs) influenced by multiple stochastic noise. An operator is constructed by averaging the spatial distributed parameters, and a comprehensive theoretical framework is developed, which can accurately describe the complex spatiotemporal dynamics of such systems.Under this framework, a rigorous operator-based Itô formula is derived, which applies to mem-ristive neural networks exhibiting reaction-diffusion behavior. By incorporating the interval matrix method, sufficient conditions for guaranteeing fixed-time mean-square exponential stabilization are obtained. Based on control cost and timeliness, and considering complex communication environments , three theorems are proposed. Finally, a simulation case is presented to analyze the control effects and costs of the controllers designed by the three theorems. Simulation results demonstrate that the proposed controllers remain effective even under network attacks.