Turing bifurcation and pattern formation of stochastic reaction-diffusion system
type: Item
instance of: scholarly article
title: Turing bifurcation and pattern formation of stochastic reaction-diffusion system
zbMATH Open document ID: 1401.37089
DOI: 10.1155/2017/9648538
author: Qianiqian Zheng
author: Zhijie Wang
author: Jianwei Shen
author: Hussain Muhammad Ather Iqbal
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS), Stochastic Reaction-Diffusion System (SRDS) is more complex and it is very difficult to deal with the noise function. In this paper, we have presented a method to solve it and obtained the conditions of how the Turing bifurcation and Hopf bifurcation arise through linear stability analysis of local equilibrium. In addition, we have developed the amplitude equation with a pair of wave vector by using Taylor series expansion, multiscaling, and further expansion in powers of small parameter. Our analysis facilitates finding regions of bifurcations and understanding the pattern formation mechanism of SRDS. Finally, the simulation shows that the analytical results agree with numerical simulation.
Mathematics Subject Classification ID: 37L55
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 6962690
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: multiscaling
zbMATH Keywords: Turing bifurcation
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/9648538
OpenAlex ID: W2587105418
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Wikidata QID: Q59142482
description: scientific article; zbMATH DE number 6962690