The operating diagram for a model of competition in a chemostat with an external lethal inhibitor

Bachir Bar (1) , Tewfik Sari (2)

1 Université de Tlemcen
2 INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

The inhibition is an important phenomenon, which promotes the stable coexistence of species, in the chemostat. Here, we study a model of two microbial species in a chemostat competing for a single resource in the presence of an external lethal inhibitor. The model is a four-dimensional system of ordinary differential equations. We give a complete analysis for the existence and local stability of all steady states. We describe the bifurcation diagram which gives the behavior of the system with respect to the operating parameters represented by the dilution rate and the input concentrations of the substrate and the inhibitor. This diagram, is very useful to understand the model from both the mathematical and biological points of view.

Mots clés: Chemostat; competition; inhibitor; stability; operating diagram

Domaines: Systèmes dynamiques [math.DS]

Bachir Bar, Tewfik Sari. The operating diagram for a model of competition in a chemostat with an external lethal inhibitor. Discrete and Continuous Dynamical Systems - Series B, 2020, 25 (6), pp.2093-2120. ⟨10.3934/dcdsb.2019203⟩. ⟨hal-01986280v2⟩