Convergence and stochastic homogenization of a class of two components nonlinear reaction-diffusion systems

We establish a convergence theorem for a class of two components nonlinear reaction-diffusion systems. Each diffusion term is the subdifferential of a convex functional of the calculus of variations whose class is equipped with the Moscoconvergence. The reaction terms are structured in such a way that the systems admit bounded solutions, which are positive in the modeling of ecosystems. As a consequence, under a stochastic homogenization framework, we prove two homogenization theorems for this class. We illustrate the results with the stochastic homogenization of a prey-predator model with saturation effect.