Exponential stabilization of spatiotemporal discrete stochastic gene regulatory networks via Weyl almost-periodic analysis and feedback control

This paper studies the dynamics and control of spatiotemporal discrete stochastic gene regulatory networks with diffusion, time delays, and Brownian perturbations. A unified discrete model is constructed by combining exponential Euler, central finite difference, and Euler–Maruyama schemes. To describe recurrent stochastic gene-expression patterns, mean-square Weyl almost periodic sequences are introduced. Under suitable Lipschitz-type assumptions, the existence and uniqueness of such solutions are established using Leray–Schauder degree theory and discrete Gronwall inequalities. An exponential-type feedback controller is further designed to ensure global exponential mean-square stabilization toward the almost-periodic trajectory. The results provide a theoretical basis for analyzing and controlling stochastic spatiotemporal gene networks and can be extended to broader diffusion-driven stochastic complex systems.