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A mathematical model of the chemostat with a general class of functions describing nutrient uptake. (English) Zbl 0569.92020
The authors consider a model of purely exploitative competition between n populations in a chemostat for a single essential nonreproducing growth limiting substrate, which may be inhibiting at high concentrations. This is in contrast to the familiar assumption of Michaelis-Menten kinetics for nutrient uptake, but includes it and all monotone increasing uptake functions. In this model, the behavior of solutions depends strongly on certain parameters.
The main result, provided that all the parameters are distinct, is that at most one of the competing populations survives. The substrate and the surviving competitor (if one exists) approach limiting values and thus there is competitive exclusion. However, the precise outcome is initial condition dependent in certain cases. A brief discussion of a potential application is given.
Reviewer: A.Hausrath

MSC:
92D25 Population dynamics (general)
92D40 Ecology
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