Dynamic renormalization group and noise induced transitions in a reaction diffusion model

We investigate how additive weak noise (correlated as well as uncorrelated) modifies the parameters of the Gray–scott reaction diffusion system by performing numerical simulations and applying a renormalization group (RG) analysis in the neighborhood of the spatial scale where biochemical reactions take place. One can obtain the same sequence of spatial–temporal patterns by means of two equivalent routes: (i) by increasing only the noise intensity and keeping all other model parameters fixed; or (ii) keeping the noise fixed, and adjusting certain model parameters to their running scale-dependent values as predicted by the RG. This explicit demonstration validates the dynamic RG transformation for finite scales in a two-dimensional stochastic model and provides further physical insight into the coarse-graining analysis proposed by this scheme. Through several study cases we explore the role of noise and its temporal correlation in self-organization and propose a way to drive the system into a new desired state in a controlled way.