Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

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 es...

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Bibliographic Details
Published in:Discrete dynamics in nature and society 2019-01, Vol.2019 (2019), p.1-15
Main Authors: Li, Yajie, Meng, Xinzhu
Format: Article
Language:English
Subjects:
Analysis
Applied mathematics
Computer simulation
Differential equations
Endangered & extinct species
Endangered species
Extinction
Growth
Liapunov functions
Mathematical functions
Mathematical models
Microorganisms
Noise
Numerical analysis
Pollution
Population
Statistical mechanics
Survival analysis
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2019/5498569