The effect of parameters on positive solutions and asymptotic behavior of an unstirred chemostat model with B–D functional response

This paper deals with the effect of parameters on properties of positive solutions and asymptotic behavior of an unstirred chemostat model with the Beddington–DeAngelis (denote by B–D) functional response under the Robin boundary condition. Firstly, we establish some a priori estimates and a sufficient condition for the existence of positive solutions (see (Feng et al. in J. Inequal. Appl. 2016(1):294, 2016)). Secondly, we study the effect of the small parameter k 1 $k_{1}$ and sufficiently large k 2 $k_{2}$ in B–D functional response, which shows that the model has at least two positive solutions. Thirdly, we investigate the case of sufficiently large k 1 $k_{1}$ . The results show that if k 1 $k_{1}$ is sufficiently large, then the positive solution of this model is determined by a limiting equation. Finally, we present an asymptotic behavior of solutions depending on time. The main methods used in this paper include the fixed point index theory, bifurcation theory, perturbation technique, comparison principle, and persistence theorem.