Stabilization of the chemostat system with mutations and application to microbial production

In this article, we consider the chemostat system with n ≥ 1 $$ n\ge species, one limiting substrate, and mutations between species. Our objective is to globally stabilize corresponding dynamical around a desired equilibrium point. Doing so, introduce auxostat feedback controls which are controllers allowing regulation of substrate concentration. We prove that such resulting closed-loop near This result obtained by combining theory asymptotically autonomous systems an explicit computation solutions limit system. The performance illustrated on optimal control problem Lagrange type consists in maximizing production species over given time period w.r.t. dilution rate chosen as variable.