Bifurcation Analysis of a Chemostat Model with a Distributed Delay

A chemostat model of a single species feeding on a limiting nutrient supplied at a constant rate is proposed. The model incorporates a general nutrient uptake function and a distributed delay. The delay indicates that the growth of the species depends on the past concentration of nutrient. Using the average time delay as a bifurcation parameter, it is proven that the model undergoes a sequence of Hopf bifurcations. Stability criteria for the bifurcating periodic solutions are derived. It is also found that the periodic solutions become unstable if the dilution rate is increased. Computer simulations illustrate the results.