(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we propose an impulsive chemostat model with microbial competition and nonlinear perturbation. First, thresholds for the extinction of both microorganisms are given. Second, we investigate the persistence in mean and boundedness of the chemostat system by constructing Lyapunov function. Moreover, we obtain the sufficient condition for the existence of an ergodic stationary distribution of the system. At last, numerical simulations are presented, and the results show that the competition between two species tends to make one species disappear from their common habitat, especially when the competition is concentrated in a single resource.