Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems

TL;DR

This paper investigates how intrinsic noise can induce Turing patterns in stochastic reaction-diffusion systems, providing a theoretical framework and computational tools to analyze noise-driven pattern formation.

Contribution

It introduces a linear noise approximation leading to a coupled multi-agent system framework for understanding noise-induced Turing patterns.

Findings

Effective computational method for spatial power spectrum analysis.

Numerical validation of noise-induced pattern formation.

Theoretical explanation via H2 norm interpretation.

Abstract

This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system.