Limit cycles in a chemostat with general variable yields and growth rates
type: Item
instance of: scholarly article
title: Limit cycles in a chemostat with general variable yields and growth rates
zbMATH Open document ID: 1115.34042
author: Edward H. C. Chang
author: Xun-Cheng Huang
author: Le-Min Zhu
published in: Nonlinear Analysis. Real World Applications
publication date: 2007-02-13T00:00:00Z
review text: The paper investigates a three-dimensional chemostat model whose variables are the concentrations of one nutrient \(S\) and two microorganisms \(x\) and \(y\) competing for this nutrient. The coefficients describing the yields and the growth rates of the microorganisms are assumed to be functions of \(S\). The authors are mainly interested in the existence and properties of periodic solutions. They show that the positive octant is positively invariant. And since, moreover, the boundary faces \(x=0\) and \(y=0\) are invariant, they may restrict the investigation to these two-dimensional problems where the Poincaré-Bendixson theorem can be applied to prove the existence of periodic orbits. Furthermore, Hopf bifurcation occurs on the two boundary faces. A numerical example illustrates the results. All proofs are rather elementary.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5125036
zbMATH Keywords: variable yield
zbMATH Keywords: Hopf bifurcation
reviewed by: Josef Hainzl
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2005.06.007
OpenAlex ID: W2020796234
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DOI: 10.1016/J.NONRWA.2005.06.007
description: scientific article; zbMATH DE number 5125036