Coexistence and stability of an unstirred chemostat model with Beddington–DeAngelis function

This paper deals with an unstirred chemostat model with the Beddington–DeAngelis functional response. First, a sufficient condition to the existence of positive steady state solutions is established. Second, the effect of the parameter β1 in the Beddington–DeAngelis functional response which models mutual interference between species u is considered. The result shows that if β1 is sufficiently large, the solution of this model is determined by a limiting equation. The main tool used here includes the fixed point index theory, the perturbation technique and the bifurcation theory.