Analyse mathématique d'un modèle de digestion anaérobie à trois étapes

Abstract

In this work, we focus on the mathematical analysis of a model of chemostat with enzymatic degradation of a substrate (organic matter) that can partly be under a solid form [7]. The study of this 3-step model is derived from a smaller order sub-model since some variables can be decoupled from the others. We study the existence and the stability of equilibrium points of the sub-model considering monotonic growth rates and distinct dilution rates. In the classical chemostat model with monotonic kinetics, it is well known that only one equilibrium point attracts all solutions and that bistability never occurs [8]. In the present study, although only monotonic growth rates are considered, it is shown that the considered sub-model may exhibit bistability. The study of 3-step model shows the existence at most four positive equilibrium whose one is locally asymptotically stable and according to the initial condition the two species can coexist.