Competition between Plasmid-Bearing and Plasmid-Free Organisms in a Chemostat with Pulsed Input and Washout

We consider a model of competition between plasmid-bearing and plasmid-free organisms in the chemostat with pulsed input and washout. We investigate the subsystem with nutrient and plasmid-free organism and study the stability of the boundary periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields the invasion threshold of the plasmid-bearing organism. By using the standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, plasmid-free, and plasmid-bearing organisms. Numerical simulations are carried out to illustrate our results.