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Multiple coexistence solutions to the unstirred chemostat model with plasmid and toxin

Published online by Cambridge University Press:  21 March 2014

HUA NIE  and
JIANHUA WU
HUA NIE
Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P.R. China email: jianhuaw@snnu.edu.cn
JIANHUA WU
Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P.R. China email: jianhuaw@snnu.edu.cn
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Abstract

We investigate the effects of toxins on the multiple coexistence solutions of an unstirred chemostat model of competition between plasmid-bearing and plasmid-free organisms when the plasmid-bearing organism produces toxins. It turns out that coexistence solutions to this model are governed by two limiting systems. Based on the analysis of uniqueness and stability of positive solutions to two limiting systems, the exact multiplicity and stability of coexistence solutions of this model are established by means of the combination of the fixed-point index theory, bifurcation theory and perturbation theory.

Keywords

ChemostatToxinCoexistence solutionPerturbation theoryMultiplicity

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 4 , August 2014 , pp. 481 - 510
Copyright
Copyright © Cambridge University Press 2014 

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