Asymptotic behaviour of the chemostat model with delayed response in growth

The asymptotic behaviour of solutions of the model for competition between three microorganisms in the chemostat is studied. The model incorporates time delays that allow for cellular components of each competing species to be structured to include unassimilated or stored nutrient and allow uptake functions to be nonmonotone. By introducing three auxiliary functions and using a lemma, it is shown that at most one competitor survives, and the substrate and the surviving competitor (if two exist) approach limiting values.