Quadratic autocatalysis with non-linear decay
type: Item
instance of: scholarly article
title: Quadratic autocatalysis with non-linear decay
zbMATH Open document ID: 1307.80007
author: Ahmed Hussein Msmali
author: M. I. Nelson
author: Maureen P. Edwards
publication date: 2014-10-09T00:00:00Z
review text: Steady state solutions are sought for model equations of a chemical process in a continuously stirred tank. It is governed by quadratic autocatalysis with a nonlinear catalyst decay. The pertinent model static and dynamics behavior has been previously investigated numerically by using path-following techniques [\textit{J. Brindley} et al., Proc. R. Soc. Lond., Ser. A 417, No. 1853, 463--496 (1988; Zbl 0652.92025)]. The main contribution of the present paper is the application of singularity theory and degenrate Hopf-bifurcation theory to obtain analytical representations for the cusp, isola, double zero and double Hopf point singularities. The bifurcation diagram is obtained that way. Various critical values have been deduced. General criterions were established for static multiplicity and periodic solutions.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 92E20
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 6353112
zbMATH Keywords: isothermal autocatalytic reactions
zbMATH Keywords: flow reactor
zbMATH Keywords: steady state solutions
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: singularity theory
zbMATH Keywords: cusp singularity
zbMATH Keywords: dynamic multiplicity
zbMATH Keywords: steady state diagrams
MaRDI profile type: Publication
full work available at URL: s10910-014-0382-5
OpenAlex ID: W2014432661
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DOI: 10.1007/S10910-014-0382-5
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 6353112