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
competition mode. nutrient recycling. time delay. Liapunov functional.
AMS Subject Classification (1991)
Primary: 34K15, 34K20, 92A15
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Sydney Mathematics and Statistics