Extensions of the chemostat model with flocculation

TL;DR

This paper extends the chemostat model to include bacterial flocculation, deriving a reduced model that captures fast flocculation dynamics and showing it can exhibit bistability under certain conditions.

Contribution

It introduces a generalized chemostat model incorporating flocculation, linking it to existing models, and analyzes its stability and bifurcation properties.

Findings

Reduced model depends on species density and growth functions.

Bistability can occur with monotonic growth rates.

Classical chemostat bistability requires non-monotonic growth.

Abstract

In this work, we study a model of the chemostat where the species are present in two forms, isolated bacteria and under an aggregated form like attached bacteria or bacteria in flocks. We show that our general model contains a lot of models which were previously considered in the literature. Assuming that flocculation and deflocculation dynamics are fast with respect to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bistability, while it may only occur in the classical chemostat model when the growth rate in non monotonic.