Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which imp...
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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: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/720283 |
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| _version_ | 1832562376614871040 |
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| author | Haihong Li Daqing Jiang Fuzhong Cong Haixia Li |
| author_facet | Haihong Li Daqing Jiang Fuzhong Cong Haixia Li |
| author_sort | Haihong Li |
| collection | DOAJ |
| description | We analyze a predator prey model with stochastic perturbation. First, we
show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results. |
| format | Article |
| id | doaj-art-04447c99c7e645728d8ffe46d31be19c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-04447c99c7e645728d8ffe46d31be19c2025-02-03T01:22:47ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/720283720283Persistence and Nonpersistence of a Predator Prey System with Stochastic PerturbationHaihong Li0Daqing Jiang1Fuzhong Cong2Haixia Li3College of Science, China University of Petroleum (East China), Qingdao 266580, ChinaCollege of Science, China University of Petroleum (East China), Qingdao 266580, ChinaDepartment of Basic Courses, Air Force Aviation University, Changchun, Jilin 130022, ChinaSchool of Business, Northeast Normal University, Changchun, Jilin 130024, ChinaWe analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.http://dx.doi.org/10.1155/2014/720283 |
| spellingShingle | Haihong Li Daqing Jiang Fuzhong Cong Haixia Li Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation Abstract and Applied Analysis |
| title | Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation |
| title_full | Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation |
| title_fullStr | Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation |
| title_full_unstemmed | Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation |
| title_short | Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation |
| title_sort | persistence and nonpersistence of a predator prey system with stochastic perturbation |
| url | http://dx.doi.org/10.1155/2014/720283 |
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