Global stability in chemostat-type competition models with nutrient recycling

Freedman and Xu [J. Math. Biol., 31 (1993), pp. 513-527] proposed two chemostat-type competition models with nutrient recycling. In the first model the recycling is instantaneous, whereas in the second, the recycling is delayed. They carried out the equilibrium analysis and obtained persistence criteria for the models. In this paper, by applying the method of Liapunov functionals we study the global asymptotic stability of the positive equilibria of the models. We also generalize the results to the multispecies competition models with instantaneous and delayed nutrient recycling, respectively. Differing from the dynamics of the usual chemostat models, we find that the competing populations could coexist if there is nutrient recycling and they compete directly.