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

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.