Polytopic Lyapunov functions for the stability analysis of persistence of competing species

Frédéric F. Grognard (1) , Frédéric F. Mazenc (2) , Alain Rapaport (2)

1 COMORE - Modeling and control of renewable resources
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

We show that intra-specific competition can explain coexistence of several species in a chemostat where they compete for a single substrate. It is indeed known that, without such a competition, only one of the species will survive. The proof technique, which is based on the construction of a polytopic Lyapunov function, is then used to extend this result to a more general class of systems.

Mots clés: SURVIVAL OF SPECIES; BIOLOGIE DES POPULATIONS; COEXISTENCE DES ESPECES; STABILITE; COMPETITION; STABILITY; LYAPUNOV FUNCTION; CHEMOSTAT; SPECIES COEXISTENCE

Domaines: Systèmes dynamiques [math.DS]; Ecologie, Environnement

Frédéric F. Grognard, Frédéric F. Mazenc, Alain Rapaport. Polytopic Lyapunov functions for the stability analysis of persistence of competing species. 44th IEEE Conference on Decision and Control, Dec 2005, Seville, Spain. pp.3699-3704, ⟨10.1109/CDC.2005.1582737⟩. ⟨hal-00999811⟩