The Chemostat Model with Lateral Gene Transfer and Distinct Removal Rates
Résumé
We investigate the classical chemostat model when lateral gene transfer is taken into account and the removal rates of the strains are distinct. We extend some results of the existing literature, obtained in the case of two strains and also in the general case, when the removal rates are equal to the dilution rate of the chemostat. We show the existence and uniqueness of the coexistence equilibrium at which all strains coexist, provided that the input concentration of the chemostat exceeds a critical value, that can be computed explicitly. We show that when the different genotypes have equal growth rate functions, then the coexistence equilibrium is globally asymptotically stable. When all yields are equal and the removal rates are equal to the dilution rate, the system satisfies the conservation principle and can be reduced to an $n$-dimensional system, where $n$ is the number of strains. We show that for $n=3$, the positive equilibrium can be unstable, with appearance of Hopf bifurcations and limit cycles. Such behavior does not occur in the two-strain case.
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