Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model
type: Item
instance of: scholarly article
title: Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model
zbMATH Open document ID: 1191.35043
author: Linglong Du
author: Mingxin Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-03-29T00:00:00Z
review text: The authors have investigated the rich by Turing instability and bifurcation phenomena dynamics of the Neumann problem for the Lengyel-Epstein reaction-diffusion system \[ \left.\begin{aligned} &u_t=\Delta u+a-u-\frac{4uv}{1+u^2}\\ &v_t=c\Delta v+b\left(u-\frac{uv}{1+u^2}\right)\end{aligned}\right\} \quad x\in\Omega, \] \[ \frac{\partial u}{\partial \nu}=\frac{\partial v}{\partial \nu}=0,\qquad x\in\partial\Omega, \qquad \qquad \] (\(\Omega\) is a bounded domain with sufficiently smooth boundary \(\partial\Omega\), \(a\), \(b\) and \(c\) are positive constants) with the aim to find spatially non-homogeneous periodic solutions, i.e., periodic solutions caused by diffusion.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 37L10
Mathematics Subject Classification ID: 58E07
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 5687651
zbMATH Keywords: Lengyel-Epstein model
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: non-homogeneous periodic solutions
zbMATH Keywords: Neumann problem
reviewed by: Oleg V. Makeev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.02.002
OpenAlex ID: W2052727578
cites work: Q3930015
cites work: Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model
cites work: Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
cites work: Turing patterns in the Lengyel-Epstein system for the CIMA reaction
cites work: Diffusion-driven instability and bifurcation in the Lengyel-Epstein system
cites work: Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system
cites work: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
DOI: 10.1016/J.JMAA.2010.02.002
description: scientific article; zbMATH DE number 5687651