Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established...

Dynamic Behaviors in a Droop Model for Phytoplankton Growth in a Chemostat with Nutrient Periodically Pulsed Input

Stability in chemostat equations with delayed nutrient recycling.

The growth of a species feeding on a limiting nutrient supplied at a constant rate is modelled by chemostat-type equations with a general nutrient uptake function and delayed nutrient recycling. Conditions for boundedness of the solutions and the existence of non-negative equilibria are given for the integrodifferential equations with distributed time lags. When the time lags are neglected cond...

Global Stability in Chemostat-Type Competition Models with Nutrient Recycling

Freedman and Xu [J. Math. Biol., 31 (1993), pp. 513–527] proposed two chemostattype 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 gl...

Global stability in chemostat-type plankton models with delayed nutrient recycling

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...