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

Source: [Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems](<https://www.sota2.com/research/paper/68fa5ebf1e209131ce9e4dbb>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-04T05:02:01.984Z

Authors: Yutaka Hori, Shinji Hara

Published: 2013-01-02T05:38:34.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1301.0170>)

[PDF](<https://arxiv.org/pdf/1301.0170.pdf>)