Dynamics of competing species in a reaction-diffusive chemostat model with an internal inhibitor

This paper investigates the unstirred chemostat model in the presence of an internal inhibitor. The primary objective is to establish the threshold dynamics of this system concerning inhibitor parameters, growth rates and diffusion rates. The theoretical analysis indicates the existence of several critical curves, which categorize the dynamics into three scenarios: (1) extinction of both species; (2) competitive exclusion; and (3) coexistence. Additionally, the numerical results reveal a tradeoff driven coexistence mechanism influenced by relevant parameters. Notably, the bistable phenomenon consistently arises due to the effects of inhibitors. Finally, we examine the impact of diffusion rates on the competitive outcomes of the two species across different competition scenarios. These new findings may have significant biological implications for the interactions between the two species competing in the unstirred chemostat model with an internal inhibitor.