Mathematical Analysis of a Stochastic Reaction-Diffusion Predator-Prey System with Prey-Taxis under Environmental Uncertainty
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This paper presents a rigorous mathematical analysis of a nonlinear stochastic reaction-diffusion system describing predator-prey dynamics incorporating prey-taxis and environmental noise. We establish the existence of weak martingale solutions via a Faedo-Galerkin approximation scheme combined with stochastic compactness arguments. The nonnegativity of the solutions is ensured through a stochastic adaptation of Stampacchia’s truncation method. Furthermore, uniqueness is obtained by means of a duality-based approach. Finally, we complement the theoretical results with two-dimensional numerical simulations that illustrate the influence of stochastic perturbations on the system’s behavior.