Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate
We present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different condi...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/423154 |
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| _version_ | 1832549283758342144 |
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| author | Chaoqun Xu Sanling Yuan Tonghua Zhang |
| author_facet | Chaoqun Xu Sanling Yuan Tonghua Zhang |
| author_sort | Chaoqun Xu |
| collection | DOAJ |
| description | We present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results. |
| format | Article |
| id | doaj-art-0e19062022464c108d2a709e388659e6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0e19062022464c108d2a709e388659e62025-02-03T06:11:42ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/423154423154Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution RateChaoqun Xu0Sanling Yuan1Tonghua Zhang2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaMathematics, FEIS, Swinburne University of Technology, P.O. Box 218 (H38) Hawthorn, VIC 3122, AustraliaWe present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results.http://dx.doi.org/10.1155/2013/423154 |
| spellingShingle | Chaoqun Xu Sanling Yuan Tonghua Zhang Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate Abstract and Applied Analysis |
| title | Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate |
| title_full | Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate |
| title_fullStr | Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate |
| title_full_unstemmed | Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate |
| title_short | Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate |
| title_sort | asymptotic behavior of a chemostat model with stochastic perturbation on the dilution rate |
| url | http://dx.doi.org/10.1155/2013/423154 |
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