Influence of diffusion on the stability of a full Brusselator model
type: Item
instance of: scholarly article
title: Influence of diffusion on the stability of a full Brusselator model
zbMATH Open document ID: 1409.35113
DOI: 10.4171/RLM/827
author: F. Capone
author: Roberta De Luca
author: Isabella Torcicollo
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2019-03-05T00:00:00Z
review text: Summary: The classic Brusselator model consists of four reactions involving six components A, B, D, E, X, Y. In a typical run, the final products \(D\) and \(E\) are removed instantly, while, the concentrations of the reactants A and B are kept constant. Then, the classic Brusselator model consisting of two equations for the intermediate X and Y is obtained. When the component B is not considered constant, it is added to the mixture and the so-called full Brusselator model is considered. In this paper, the full Brusselator model is studied. In particular, the boundedness of solutions and the effect of diffusion on the linear stability is analyzed. Moreover, sufficient conditions ensuring that the unique steady state, unstable (stable) in the ODEs system, becomes stable (unstable) in presence of diffusion, are performed and a first nonlinear stability result is obtained.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B36
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 7032417
zbMATH Keywords: reaction-diffusion systems
zbMATH Keywords: Brusselator model
zbMATH Keywords: stability
zbMATH Keywords: Turing instability
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/rlm/827
OpenAlex ID: W2907476374
Wikidata QID: Q128667353
description: scientific article; zbMATH DE number 7032417