Abstract
We propose a new stochastic competition chemostat system with saturated growth rate and impulsive toxicant input. The main purpose of this paper is to study the stochastic dynamics of a high-dimensional impulsive stochastic chemostat model and find the threshold between persistence and extinction for the impulsive stochastic chemostat system. First, we investigate the stability of the periodic solution of a deterministic impulsive chemostat model and obtain the threshold between persistence and extinction for the system. Second, by using qualitative analysis method of impulsive stochastic differential equations, we obtain conditions for the extinction and persistence in mean of two microorganisms in the stochastic chemostat model. The results show that a stochastic disturbance or the impulsive effect can cause the microorganisms to go to extinction. Finally, we provide some examples together with numerical simulations to illustrate the analytical results and explain the biological implications.
Highlights
The chemostat is a kind of experimental device that can be used to cultivate microorganisms and plays an important role in many fields, such as microbiology, ecology, chemical engineering, and so on
We explore the threshold between the extinction and persistence of two microorganisms and study the influences of impulsive toxicant input and stochastic disturbance on system dynamics
4 Conclusion and simulations In this paper, we investigate the dynamics of an impulsive stochastic competition chemostat model with saturated growth rate in a polluted environment
Summary
The chemostat is a kind of experimental device that can be used to cultivate microorganisms and plays an important role in many fields, such as microbiology, ecology, chemical engineering, and so on. Some scholars have studied the dynamics behaviors of various kinds of stochastic systems and obtained many good results [ – ] Taking both impulsive toxicant input and white noises into account, persistence and extinction of a singlespecies population system in a polluted environment with random perturbations and impulsive toxicant input were explored [ , ]. To capture essential features of the processes, the following several aspects should be considered in the formulation of chemostat models: (a) two-species competition for a limiting nutrient supplied at a constant rate; (b) impulsive toxicant input; (c) white noise stochastic disturbance; and (d) saturated growth rate. Based on the four aspects, we propose a new competition model with white noise disturbance and impulsive toxicant input For this new system, we explore the threshold between the extinction and persistence of two microorganisms and study the influences of impulsive toxicant input and stochastic disturbance on system dynamics. This implies that the conditions for xi(t) to go to extinction in the deterministic system ( ) are stronger than in the corresponding stochastic model ( )
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
