Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
type: Item
instance of: scholarly article
title: Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
zbMATH Open document ID: 1288.35051
DOI: 10.1216/RMJ-2013-43-5-1637
author: Jiayin Jin
author: Junping Shi
author: Junjie Wei
author: Fengqi Yi
published in: Rocky Mountain Journal of Mathematics
publication date: 2013-11-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1382705672
review text: The authors investigate Hopf bifurcations for a chemical 2-species reaction-diffusion equation in one spatial coordinate with Neumann boundary conditions. After an elaborate discussion of the stability of stationary solutions they carefully investigate the postcritical behaviour of the bifurcating spatially nonhomogeneous periodic solutions. Depending on a distinguished parameter the solutions bifurcate super- or subcritically. By simulating the system dynamics for various combinations of system parameters, good agreement between the analytical investigation and numerical treatment is obtained. Finally the authors summarize the necessary formulas for the calculation of the coefficients in the bifurcation equations in the appendix.
reviewed by: Alois Steindl
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 92E20
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 92B05
zbMATH DE Number: 6226526
zbMATH Keywords: Lengyel-Epstein chemical reaction
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: steady state bifurcation
zbMATH Keywords: spatially non-homogeneous periodic orbits
zbMATH Keywords: global bifurcation
zbMATH Keywords: one spatial coordinate
zbMATH Keywords: Neumann boundary conditions
MaRDI profile type: Publication
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OpenAlex ID: W2013892518
description: scientific article; zbMATH DE number 6226526