Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System
A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness o...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/963712 |
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| _version_ | 1832550018029977600 |
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| author | Shengliang Guo Zhijun Liu Huili Xiang |
| author_facet | Shengliang Guo Zhijun Liu Huili Xiang |
| author_sort | Shengliang Guo |
| collection | DOAJ |
| description | A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results. |
| format | Article |
| id | doaj-art-9346ae17c2534c1e935343d22373d741 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9346ae17c2534c1e935343d22373d7412025-02-03T06:07:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/963712963712Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive SystemShengliang Guo0Zhijun Liu1Huili Xiang2Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaKey Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaKey Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaA stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results.http://dx.doi.org/10.1155/2014/963712 |
| spellingShingle | Shengliang Guo Zhijun Liu Huili Xiang Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System Journal of Applied Mathematics |
| title | Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System |
| title_full | Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System |
| title_fullStr | Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System |
| title_full_unstemmed | Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System |
| title_short | Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System |
| title_sort | stochastically ultimate boundedness and global attraction of positive solution for a stochastic competitive system |
| url | http://dx.doi.org/10.1155/2014/963712 |
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