Résumé
In this work, we examine the benefit of having periodic dilution rate in the chemostat model in terms of averaged conversion rate. We compare the effect of bringing a same substrate quantity by a periodic rate with a constant rate. We show that for the classical chemostat model with a Contois growth function, the performance of the averaged conversion rate can be improved under certain conditions. Using Pontryagin's Principle, we characterize the extremals of the problem which minimizes the averaged substrate concentration among periodic trajectories of a given period.