The Effect of Inhibitor on the PlasmidBearing and PlasmidFree Model in the Unstirred Chemostat

This paper deals with a chemostat model with an inhibitor in the context of competition between plasmidbearing and plasmidfree organisms. First, sufficient conditions for coexistence of the steadystate are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter , which represents the effect of the inhibitor, plays a very important role in deciding the number of the coexistence solutions. The results show that if is sufficiently large this model has at least two coexistence solutions provided that the maximal growth rate a of u lies in a certain range and has only one unique asymptotically stable coexistence solution when a belongs to another range. Finally, extensive simulations are done to complement the analytic results. The main tools used here include degree theory in cones, bifurcation theory, and perturbation technique.