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 firs t model the recycling is instantaneous, whereas in the second, the rec ycling is delayed. They carried out the equilibrium analysis and obtai ned persistence criteria for the models. In this paper, by applying th e method of Liapunov functionals we study the global asymptotic stabil ity of the positive equilibria of the models. We also generalize the r esults to the multispecies competition models with instantaneous and d elayed nutrient recycling, respectively. Differing from the dynamics o f the usual chemostat models, we find that the competing populations c ould coexist if there is nutrient recycling and they compete directly.