Global periodic solutions for a differential delay system modeling a microbial population in the chemostat
type: Item
instance of: scholarly article
title: Global periodic solutions for a differential delay system modeling a microbial population in the chemostat
zbMATH Open document ID: 0833.34069
author: Tao Zhao
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-11-01T00:00:00Z
review text: The author studies the differential delay system modeling a microbial population in the chemostat \[ \dot s(t)= 1- s(t)- P(s(t))u(t),\quad \dot u(t)= [- 1+ P(S((t- \tau))].\tag{1} \] The author gives a sufficient conditions that the washout steady state (\(u= 0\), \(S= 1\)) is globally stable and establishes sufficient conditions for the global existence of a periodic solution by proving the existence of nontrivial periodic points of an appropriate map. The author also presents an explicit application to Michaelis-Menten kinetics.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 811591
zbMATH Keywords: stability
zbMATH Keywords: differential delay system
zbMATH Keywords: microbial population in the chemostat
zbMATH Keywords: washout steady state
zbMATH Keywords: periodic solution
zbMATH Keywords: Michaelis-Menten kinetics
reviewed by: Jibin Li
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1239
OpenAlex ID: W2010861439
DOI: 10.1006/JMAA.1995.1239
description: scientific article; zbMATH DE number 811591