Fast-Diffusion Limit with Large Noise for Systems of Stochastic Reaction-Diffusion Equations

We consider a class of stochastic reaction-diffusion equations with additive noise. We show that in the limit of fast diffusion, one can approximate solutions of the SPDE by the solution of a suitable ordinary differential equation (ODE) only describing the reactions. Also, we show large fluctuations lead in the limit to surprising new terms in the ODE. We focus on systems with polynomials nonlinearities and give applications to the predator-prey system and a cubic auto-catalytic reaction between two chemicals