École Nationale Supérieure de
Techniques Avancées

Abstract

Periodic solutions of the chemostat model are studied under integral constraints on the washout rate, aiming at improving average water quality. For the one-species chemostat, an optimal control, which may admit a singular arc, is synthesized for convex-concave growth functions. The optimal trajectories generalize the existing ones for convex and concave growth functions. Then, unicity of periodic positive solutions is considered. In the two-species chemostat, a non-generic counter- example were infinitely many positive periodic solutions exist is constructed. In the one-species gradostat, unicity is proven for a rather broad class of configurations. Contrary to many existing results, this result applies for any monotone growth function.