Bifurcation analysis of a chemostat model with two distributed delays
type: Item
instance of: scholarly article
title: Bifurcation analysis of a chemostat model with two distributed delays
zbMATH Open document ID: 1059.34059
author: Sanling Yuan
author: Maoan Han
published in: Chaos, Solitons and Fractals
publication date: 2004-08-19T00:00:00Z
review text: The article studies a chemostat-type model, a system of delay differential equations (DDEs) with two distributed delays as proposed by \textit{E. Beretta} and \textit{Y. Takeuchi} [Differ. Equ. Dyn. Syst. 2, No. 4, 263--288 (199; Zbl 0995.34068)]. The paper proves that the model undergoes a Hopf bifurcation when the average time delay is varied as a bifurcation parameter. The bifurcation is shown to occur for the special case of exponential kernels in the distributed delay terms, which allows a reduction of the DDE system to a system of ordinary differential equations. This result disproves the main statement of \textit{H. A. Abdallah} [Chaos Solitons Fractals 17, No. 5, 879--884 (2003; Zbl 1033.92032)].
reviewed by: Jan Sieber
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92E20
zbMATH DE Number: 2093186
zbMATH Keywords: delay differential equation
zbMATH Keywords: distributed delay
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
full work available at URL: j.chaos.2003.09.048
OpenAlex ID: W1986242353
cites work: Qualitative properties of chemostat equations with time delays: Boundedness, local and global asymptotic stability
cites work: Global Stability in Chemostat-Type Equations with Distributed Delays
cites work: Stability and persistence in plankton models with distributed delays.
cites work: The Theory of the Chemostat
cites work: Delay differential equations: with applications in population dynamics
cites work: Stability in chemostat equations with delayed recycling
cites work: Effects of time lags on transient characteristics of a nutrient cycling model
cites work: The effect of delays on stability and persistence in plankton models
cites work: Global stability in chemostat-type plankton models with delayed nutrient recycling
cites work: Q4189109
cites work: Q4138551
cites work: Q4312237
cites work: Bifurcation analysis of a chemostat model with a distributed delay
cites work: Coexistence in a Model of Competition in the Chemostat Incorporating Discrete Delays
DOI: 10.1016/J.CHAOS.2003.09.048
description: scientific article; zbMATH DE number 2093186