Global stability in chemostat-type plankton models with delayed nutrient recycling
Xue-zhong He and Shigui Ruan
Research Report 96-8
Date: February 1996
In this paper, we consider chemostat-type plankton models in which plankton
feeds on a limiting nutrient and the nutrient is supplied at a constant rate
and is partially recycled after the death of plankton by bacterial
decomposition. We use a distributed delay to describe nutrient recycling and
a discrete delay to model the planktonic growth response to nutrient uptake.
When one or both delays occur, by constructing Liapunov functionals, we obtain
some sufficient conditions for the global stability of the positive
equilibrium, which can be regarded as estimates of the delays for persistence
of global stability.
plankton models. nutrient recycling. time delay. Liapunov functionals.
AMS Subject Classification (1991)
Primary: 34D05, 34C25, 34K20, 92A1
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Sydney Mathematics and Statistics