We study a model of the chemostat with several species in competition for a single resource. We take into account the intra-specific interactions between individuals of the same population of micro-organisms and we assume that the growth rates are increasing and the dilution rates are distinct. Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria. Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium. Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species. The operating diagram describes the asymptotic behavior of this model with respect to control parameters and illustrates the effect of the intra-specific competition on the coexistence region of the species.
a b s t r a c tIn this work, we study a model of the chemostat where the species are present in two forms, isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. We show that our general model contains a lot of models that were previously considered in the literature. Assuming that flocculation and deflocculation dynamics is fast compared to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bi-stability, while it may occur in the classical chemostat model, but when the growth rate is nonmonotonic.
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