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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/5498569 |
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| _version_ | 1849304618586079232 |
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| author | Yajie Li Xinzhu Meng |
| author_facet | Yajie Li Xinzhu Meng |
| author_sort | Yajie Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3b85a865b9454632b0a91eea5af10e99 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3b85a865b9454632b0a91eea5af10e992025-08-20T03:55:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/54985695498569Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted EnvironmentYajie Li0Xinzhu Meng1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThis 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.http://dx.doi.org/10.1155/2019/5498569 |
| spellingShingle | Yajie Li Xinzhu Meng Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment Discrete Dynamics in Nature and Society |
| title | Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment |
| title_full | Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment |
| title_fullStr | Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment |
| title_full_unstemmed | Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment |
| title_short | Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment |
| title_sort | dynamics of an impulsive stochastic nonautonomous chemostat model with two different growth rates in a polluted environment |
| url | http://dx.doi.org/10.1155/2019/5498569 |
| work_keys_str_mv | AT yajieli dynamicsofanimpulsivestochasticnonautonomouschemostatmodelwithtwodifferentgrowthratesinapollutedenvironment AT xinzhumeng dynamicsofanimpulsivestochasticnonautonomouschemostatmodelwithtwodifferentgrowthratesinapollutedenvironment |