Persistent competition models on two complementary nutrients with density-dependent consumption rates

Abstract

We give a result of uniform persistence for a theoretical competition model of 3 species of microorganisms on 2 complementary nutrients in a chemostat with density-dependent growth functions. The proof consists of giving first sufficient conditions of persistence, which is by the way available for more than 3 species. Then, in the case of 2 species, we show under additional assumptions, and with the use of the so-called Hofbauer–Hutson theorem, that it is possible to obtain a uniform persistence around a positive equilibrium point. Finally, the main result is established from what preceeds and by means of Thieme–Zhao theorem. These results are illustrated by some numerical simulations.