Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment. (24th February 2019)

• Record Type: Journal Article
• Authors: Li, Yajie; Meng, Xinzhu
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2019(2019)
• Publication Date: 2019-02-24
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2019/5498569
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results.