Existence and stability of positive steady-state solutions for a Chemostat model

An unstirred chemostat model with Beddington-DeAngelis functional response is discussed.First,the bifurcation at the semi-trivial solution(θ,0) is obtained by using theory of eigenvalue and bifurcation.A sufficient condition for the existence of positive steady-state solutions is given.Second,it is proved that under some conditions,the positive steady-state solutions are stable by using the stability theorem on bifurcation solutions.