Stochastic Predator-Prey System Subject to Lévy Jumps
This paper investigates a new nonautonomous impulsive stochastic predator-prey system with the omnivorous predator. First, we show that the system has a unique global positive solution for any given initial positive value. Second, the extinction of the system under some appropriate conditions is exp...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/5749892 |
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| _version_ | 1832563348325007360 |
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| author | Xinzhu Meng Xiaohong Wang |
| author_facet | Xinzhu Meng Xiaohong Wang |
| author_sort | Xinzhu Meng |
| collection | DOAJ |
| description | This paper investigates a new nonautonomous impulsive stochastic predator-prey system with the omnivorous predator. First, we show that the system has a unique global positive solution for any given initial positive value. Second, the extinction of the system under some appropriate conditions is explored. In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. Simulations are also carried out to illustrate our theoretical analysis conclusions. |
| format | Article |
| id | doaj-art-2e5543474b6a442e9d5b13fbd36b56e8 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2e5543474b6a442e9d5b13fbd36b56e82025-02-03T01:20:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/57498925749892Stochastic Predator-Prey System Subject to Lévy JumpsXinzhu Meng0Xiaohong Wang1State Key Laboratory of Mining Disaster Prevention and Control Cofounded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, ChinaState Key Laboratory of Mining Disaster Prevention and Control Cofounded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, ChinaThis paper investigates a new nonautonomous impulsive stochastic predator-prey system with the omnivorous predator. First, we show that the system has a unique global positive solution for any given initial positive value. Second, the extinction of the system under some appropriate conditions is explored. In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. Simulations are also carried out to illustrate our theoretical analysis conclusions.http://dx.doi.org/10.1155/2016/5749892 |
| spellingShingle | Xinzhu Meng Xiaohong Wang Stochastic Predator-Prey System Subject to Lévy Jumps Discrete Dynamics in Nature and Society |
| title | Stochastic Predator-Prey System Subject to Lévy Jumps |
| title_full | Stochastic Predator-Prey System Subject to Lévy Jumps |
| title_fullStr | Stochastic Predator-Prey System Subject to Lévy Jumps |
| title_full_unstemmed | Stochastic Predator-Prey System Subject to Lévy Jumps |
| title_short | Stochastic Predator-Prey System Subject to Lévy Jumps |
| title_sort | stochastic predator prey system subject to levy jumps |
| url | http://dx.doi.org/10.1155/2016/5749892 |
| work_keys_str_mv | AT xinzhumeng stochasticpredatorpreysystemsubjecttolevyjumps AT xiaohongwang stochasticpredatorpreysystemsubjecttolevyjumps |