Sur les perturbations singulières dans les inclusions différentielles - Sur la compétition dans le chémostat avec inhibiteur externe

Abstract

The aim of this thesis is twofold, one is the study of perturbations of differential inclusions by the multiple scales method, the second is the study of some chemostat model with inhibition. The first is considered when we have a singular perturbation system, where an application for a resource-consumer model is considered, And when we have a differential inclusion with maximum, where the averaging method is applied to study the limit of the solutions set. The second is the study of a chemostat model with an external inhibitor, where we analyse the equilibria of the system and construct the operating diagram. Keywords: Differential inclusions, averaging method, singular perurbation, chemostat, operating diagram.