Large scale emergent properties of an autocatalytic reaction-diffusion model subject to noise

TL;DR

This paper analyzes the stochastic Gray-Scott reaction-diffusion model using dynamic renormalization group techniques to understand emergent properties, revealing stable fixed points and noise-induced reaction terms.

Contribution

It provides an analytical study of non-equilibrium fluctuations in a stochastic reaction-diffusion model, introducing effective three-body reactions caused by noise and nonlinearities.

Findings

Identification of a stable fixed point at one-loop order

Prediction of asymptotic scaling for correlation functions

Discovery of noise-induced three-body reaction terms

Abstract

The non-equilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New effective three-body reaction terms, not present in the original GS model, are induced by the combined interplay of the fluctuations and nonlinearities.