A new proof of the competitive exclusion principle in the chemostat

Alain Rapaport (1) , Mario Veruete (2)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 IMAG - Institut Montpelliérain Alexander Grothendieck

We give an new proof of the well-known competitive exclusion principle in the chemostat model with N species competing for a single resource , for any set of increasing growth functions. The proof is constructed by induction on the number of the species, after being ordered. It uses elementary analysis and comparisons of solutions of ordinary differential equations.

Mots clés: comparison principle; global stability; competitive exclusion; chemostat model; induction

Domaines: Systèmes dynamiques [math.DS]; Ecosystèmes

Alain Rapaport, Mario Veruete. A new proof of the competitive exclusion principle in the chemostat. Discrete and Continuous Dynamical Systems - Series B, 2019, 24 (8), pp.3755-3764. ⟨10.3934/dcdsb.2018314⟩. ⟨hal-01834770⟩