Properties of the Chemostat Model with Aggregated Biomass and Distinct Removal Rates

Understanding and exploiting the flocculation process is a major challenge in the mathematical theory of the chemostat. Here, we study a model of the chemostat involving the flocculating and deflocculating dynamics of planktonic and attached biomass competing for a single nutrient. In our study, the mortality (or maintenance) of species is taken into account and not neglected as in previous studies. The model is a three-dimensional system of ordinary differential equations. Using general monotonic functional responses, we give a complete analysis for the existence and local stability of all steady states. The theoretical analysis of the model involving the mortality is a difficult problem since the model is not reduced to a planar system as in the case where the dilution rates of the substrate and the biomass are equal. With the same dilution rates, it is well known that the model can have a positive steady state which is unique and stable as long as it exists. Without mortality, and different dilution ra...