Feedback control for nonmonotone competition models in the chemostat

This paper deals with the problem of feedback control of competition between two species with one substrate in the chemostat with nonmonotone growth functions. Without control, the generic behavior is competitive exclusion. The aim of this paper is to find a feedback control of the dilution rate, depending only on the total biomass, such that coexistence holds. We obtain a sufficient condition for the global asymptotic stability of a unique equilibrium point in the positive orthant for a three-dimensional differential system which arises from this controlled competition model. This paper generalizes the results obtained by De Leenheer and Smith in (J. Math. Biol. 46 (2003) 48).