Global stability in chemostat-type competition models with nutrient recycling


Shigui Ruan and Xue-zhong He


Research Report 96-9
Date: February 1996


(Freedman and Xu (J. Math. Biol. 31(1993), 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 multi-species 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.

Key phrases

competition mode. nutrient recycling. time delay. Liapunov functional. global stability.)

AMS Subject Classification (1991)

Primary: 34K15, 34K20, 92A15


The paper is available in the following forms:
PostScript: (98kB) or (439kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics