A FLOCCULATION MODEL IN THE CHEMOSTAT WITH DISTINCT REMOVAL RATES AND YIELDS

In this paper, a flocculation model is considered in a chemostat with a single resource and one species in two forms: planktonic and aggregated bacteria. The removal rates are distinct and include the specific death rates. Considering distinct yield coefficients with a large class of growth rates, we present a mathematical analysis of the model by establishing the necessary and sufficient conditions of existence and local asymptotic stability of all equilibria. From these conditions, we first theoretically determine the operating diagram describing the asymptotic behavior of the system according to two operating parameters. The bifurcation analysis shows a rich behavior: transcritical, saddle-node, Hopf, and homoclinic bifurcations. Using the numerical method with MATCONT software, we detect fold bifurcation points of two stable and unstable limit cycles that emerge through supercritical and subcritical Hopf bifurcations, as well as two-parameter bifurcations such as Bogdanov–Takens, Cusp, and Generalized Hopf bifurcations. Our analysis shows that the flocculation process promotes the coexistence of isolated and attached bacteria around a stable limit cycle or positive equilibrium. These theoretical messages explain and reinforce the experimental observations about the positive effect of flocculation on the maintenance of species coexistence and the protection of the most relevant species among microbial ecosystems.