A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input ☆

In this paper, we present and analyze a simple model for a chemostat with plasmid-bearing and plasmid-free organisms and periodically pulsed substrate. We obtain an exact periodic solution with positive concentrations of substrate and plasmid-free organism, and furthermore, we prove that the periodic solution is stable if the impulsive period is more than some critical value and meanwhile we prove that system is permanent if the impulsive period is less than some critical value. Finally, we give a brief discussion and find that periodically pulsed input destroys the equilibria of the unforced continuous system.