Analysis of the Droop Model with Wall Growth in a Chemostat

Abstract

In this paper, we construct a simple chemostat-based variable yield model of competition between two bacterial strains, one of which is capable of wall growth [14]. In this model we prove the boundedness of solutions, analyze the local stability of equilibria and establish the global stability for the locally stable extinction equilibrium. Furthermore, when the extinction equilibrium becomes unstable, we prove the existence and uniqueness of the positive equilibrium and the uniform persistence of the system.