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Pré-Publication, Document De Travail Mathematical Biosciences Année : 2018

A MODEL OF TWO COMPETITORS IN A CHEMOSTAT WITH AN EXTERNAL INHIBITOR

Résumé

A model of two microbial species in a chemostat competing for a single resource in the presence of an external inhibitor is considered. This model was previously considered only in the case where the growth rate functions and the absorption rate of inhibitor are Michaelis-Menten or Monod kinetics. In this paper, we consider the general case of monotonic functions. Through the three operating parameters of the system represented by the dilution rate and the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for the existence and stability of all equilibria. By means of operating diagrams, we describe the asymptotic behavior of the model with respect to those operating parameters. Some examples are given to illustrate the mathematical results corresponding to cases where the growth rates are of Monod or Holling types.
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Dates et versions

hal-01573559 , version 1 (09-08-2017)
hal-01573559 , version 2 (16-05-2020)

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Citer

Mohamed Dellal, Mustapha Lakrib, Tewfik Sari. A MODEL OF TWO COMPETITORS IN A CHEMOSTAT WITH AN EXTERNAL INHIBITOR. 2017. ⟨hal-01573559v1⟩

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