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.

This paper deals with the mathematical study of a new nonlinear forager-exploiter-fluid system that characterizes the interactions between two predators and prey in a Newtonian fluid medium. Weak solutions for the proposed system are established based on the Schauder fixed-point theory, a priori estimates, and compactness arguments. Finally, we provide the numerical simulation for the proposed model in two-dimensional spatial settings.