  We investigate how additive weak noise (correlated as well as uncorrelated)
modifies the parameters of the Gray-Scott (GS) 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.
