Global analysis of a new nonlinear stochastic differential competition system with impulsive effect

Advances in Difference Equations

Xuejin Lv¹  Xinzhu Meng¹  Lu Wang² 

[1] College of Mathematics and Systems Science, Shandong University of Science and Technology;Huangdao Sixteenth Middle School;

关键词: stochastic chemostat system;    impulsive toxicant input;    Itô’s formula;    persistence in mean;    nonlinear growth rate;   

DOI  :  10.1186/s13662-017-1363-3

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown