Dynamic Renormalization Group and Noise Induced Transitions in a Reaction Diffusion Model
Abstract
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.
Cite
@article{arxiv.cond-mat/0507139,
title = {Dynamic Renormalization Group and Noise Induced Transitions in a Reaction Diffusion Model},
author = {M. -P. Zorzano and D. Hochberg and F. Moran},
journal= {arXiv preprint arXiv:cond-mat/0507139},
year = {2007}
}
Comments
8 pages, 21 figures