International Journal of Differential Equations

A Predator-Prey Model in the Chemostat with Time Delay

Guihong Fan and Gail S. K. Wolkowicz

Full-text: Open access

Abstract

The aim of this paper is to study the dynamics of predator-prey interaction in a chemostat to determine whether including a discrete delay to model the time between the capture of the prey and its conversion to viable biomass can introduce oscillatory dynamics even though there is a globally asymptotically stable equilibrium when the delay is ignored. Hence, Holling type I response functions are chosen so that no oscillatory behavior is possible when there is no delay. It is proven that unlike the analogous model for competition, as the parameter modeling the delay is increased, Hopf bifurcations can occur.

Article information

Source
Int. J. Differ. Equ., Volume 2010, Special Issue (2010), Article ID 287969, 41 pages.

Dates
Received: 1 November 2009
Accepted: 11 January 2010
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399837

Digital Object Identifier
doi:10.1155/2010/287969

Mathematical Reviews number (MathSciNet)
MR2607726

Zentralblatt MATH identifier
1207.34105

Citation

Fan, Guihong; Wolkowicz, Gail S. K. A Predator-Prey Model in the Chemostat with Time Delay. Int. J. Differ. Equ. 2010, Special Issue (2010), Article ID 287969, 41 pages. doi:10.1155/2010/287969. https://projecteuclid.org/euclid.ijde/1485399837


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