Time-varying control laws with guaranteed persistence for a class of multi-species chemostat models with different removal rates

In this paper, a class of chemostat models with N species compete for a limited nutrient with different removal rates is investigated. First, three assumptions are given to guarantee the existence of stabilizable periodic trajectories. Then a time-varying feedback for dilution rate and input substrate is designed, so that a positive trajectory of the chemostat model is globally asymptotically stable.