Competition for one resource with internal storage and inhibitor in an unstirred chemostat

Abstract

This paper deals with a mathematical model of two species competing for one resource in an unstirred chemostat with internal storage and inhibitor. First, the well-posedness of the competition model is established. Second, the threshold dynamics of the single population model is determined by the principal eigenvalue of a nonlinear eigenvalue problem. Third, sufficient conditions for the asymptotic instability of trivial and semi-trivial steady state solutions are given in terms of the principal eigenvalues of the corresponding nonlinear eigenvalue problems. Furthermore, under these conditions, the system is uniformly persistent and there is at least one coexistence equilibrium. The main methods used here are the nonlinear eigenvalue problems and uniform persistence theory.