Uniqueness of positive steady state solutions to the unstirred chemostat model with external inhibitor

Abstract

A competition model of two organisms is considered in the unstirred chemostat-type system in the presence of an external inhibitor. Asymptotic stability properties of the trivial and semitrivial steady state solutions are established by spectral analysis. The stability and uniqueness of positive steady state solutions are also given by Lyapunov Schmidt procedure and perturbation technique.