Periodic behavior of the stochastic Brusselator in the mean-field limit

Abstract

We prove a “propagation of chaos” result for the mean-field limit of a model for a trimolecular chemical reaction called “Brusselator”. Then we show that the pair of nonlinear (i.e. law-dependent) stochastic differential equations describing the evolution of the concentration of the molecules at a given site in the mean field limit has a solution with a periodic law (in t). Finally we identify the limit and establish a central limit theorem for the periodic law in the case where the noise tends to zero.