Coexistence states of unstirred Chemostat model with C-M functional response

The existence and stability of the positive solutions for an unstirred Chemostat model with Crowley-Martin functional response are considered. Firstly, by means of the fixed point index theory, the sufficient conditions for the existence of the positive solutions are determined. Moreover, the stability of the local positive solutions is investigated by using the perturbation theorem for linear operators and the stability theorem for bifurcation solutions. The results indicate that the two species will coexist under certain conditions, furthermore the coexistence solutions are stable.