Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation
We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among n patches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean,...
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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/10.1155/2014/320460 |
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| _version_ | 1849413937016078336 |
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| author | Li Zu Daqing Jiang Donal O’Regan |
| author_facet | Li Zu Daqing Jiang Donal O’Regan |
| author_sort | Li Zu |
| collection | DOAJ |
| description | We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among n patches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation. |
| format | Article |
| id | doaj-art-6b0ced13984c4b81a987eb2785ca1dcc |
| 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-6b0ced13984c4b81a987eb2785ca1dcc2025-08-20T03:34:00ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/320460320460Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random PerturbationLi Zu0Daqing Jiang1Donal O’Regan2School of Science, Changchun University, Changchun 130022, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaSchool of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, IrelandWe analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among n patches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.http://dx.doi.org/10.1155/2014/320460 |
| spellingShingle | Li Zu Daqing Jiang Donal O’Regan Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation Abstract and Applied Analysis |
| title | Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation |
| title_full | Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation |
| title_fullStr | Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation |
| title_full_unstemmed | Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation |
| title_short | Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation |
| title_sort | stochastic permanence stationary distribution and extinction of a single species nonlinear diffusion system with random perturbation |
| url | http://dx.doi.org/10.1155/2014/320460 |
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