Coexistence of two species with intra- and interspecific competition in an unstirred chemostat

In this paper, we study an intra- and interspecific competition system with the different diffusion rates in an unstirred chemostat. Due to the present of the different diffusion rates, the conservation principle for a classical standard chemostat model does not hold here. Firstly, we prove the existence, the uniqueness and asymptotic behaviors of positive solution of the single population system by using the degree theory. Secondly, by the degree theory and standard bifurcation theory, the existence and global structure of the coexistence solutions are investigated. The results show that when the maximum growth rates of two microorganisms with different diffusion abilities are not small, two competing microorganisms will coexist. Finally, numerical simulations are performed to illustrate that the interspecific interference can help the weaker competitor to win in the competition.