Dynamics of an unstirred chemostat model with Beddington–DeAngelis functional response

Abstract

This paper deals with an unstirred competitive chemostat model with the Beddington–DeAngelis functional response. With the help of the linear eigenvalue theory and the monotone dynamical system theory, we establish a relatively clear dynamic classification of this system in terms of the growth rates of two species. The results indicate that there exist several critical curves, which may classify the dynamics of this system into three scenarios: 1) extinction; 2) competitive exclusion; and 3) coexistence. Comparing with the classical chemostat model [26], our theoretical results reveal that under the weak–strong competition cases, the role of intraspecific competition can lead to species coexistence. Moreover, the simulations suggest that under different competitive cases, coexistence can occur for suitably small diffusion rates and some intermediate diffusion rates. These new phenomena indicate that the intraspecific competition and diffusion have a great influence on the dynamics of the unstirred chemostat model of two species competing with the Beddington–DeAngelis functional response.