Dynamic Renormalization Group and Noise Induced Transitions in a Reaction Diffusion Model

TL;DR

This paper combines numerical simulations and renormalization group analysis to study how weak additive noise influences pattern formation in the Gray-Scott reaction-diffusion model, revealing how noise and parameter adjustments can produce similar spatial-temporal patterns.

Contribution

It demonstrates the validity of dynamic RG transformations at finite scales in a stochastic reaction-diffusion system and explores noise's role in self-organization and control of patterns.

Findings

Noise modifies system parameters via RG flow.

Pattern sequences can be replicated by noise increase or parameter adjustment.

Noise and correlation influence self-organization and state control.

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.