Stability and persistence in plankton models with distributed delays

In this paper a model with two independent distributed delays is proposed to describe a population of microorganism feeding on a limiting nutrient which is supplied at a constant rate and is recycled after the death of the species by decomposer action. We obtain sufficient conditions for local and global stability of the positive equilibrium of the model. A fairly general function for nutrient uptake is considered. Stability changes of the positive equilibrium as the nutrient supply increases are studied by the Hopf bifurcation theorem.