Taiwanese Journal of Mathematics

MODEL OF THE EFFECT OF ANTI-COMPETITOR TOXINS ON PLASMID-BEARING, PLASMID-FREE COMPETITION

Sze-Bi Hsu and Paul Waltman

Full-text: Open access

Abstract

The usual models of the chemostat assume that the competition is purely exploitative, the competition is only through the consumption of the nutrient. However, it is known that microorganisms can produce toxins against its competitors. In this work, we consider a model of competition in the chemostat between plasmid-bearing, plasmid-free organisms for a single nutrient where plasmid-bearing organism can produce a toxin (allelopathic agent) against the plasmid-free organism at some cost to its reproductive abilities. We give a characterization of the outcome of this competition in terms of the relevant parameters in hyperbolic cases. The global asymptotic behavior of the solutions is proved by using the perturbation of a globally stable steady state for a sufficiently small plasmid loss rate.

Article information

Source
Taiwanese J. Math., Volume 6, Number 1 (2002), 135-155.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407405

Digital Object Identifier
doi:10.11650/twjm/1500407405

Mathematical Reviews number (MathSciNet)
MR1884460

Zentralblatt MATH identifier
1029.34038

Subjects
Primary: 34D05: Asymptotic properties 34D20: Stability 92D25: Population dynamics (general)

Keywords
competition chemostat plasmid-bearing plasmid-free perturbation of a globally stable steady state

Citation

Hsu, Sze-Bi; Waltman, Paul. MODEL OF THE EFFECT OF ANTI-COMPETITOR TOXINS ON PLASMID-BEARING, PLASMID-FREE COMPETITION. Taiwanese J. Math. 6 (2002), no. 1, 135--155. doi:10.11650/twjm/1500407405. https://projecteuclid.org/euclid.twjm/1500407405


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