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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Main Authors: Li Zu, Daqing Jiang, Donal O’Regan
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/320460
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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.
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institution Kabale University
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language English
publishDate 2014-01-01
publisher Wiley
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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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AT daqingjiang stochasticpermanencestationarydistributionandextinctionofasinglespeciesnonlineardiffusionsystemwithrandomperturbation
AT donaloregan stochasticpermanencestationarydistributionandextinctionofasinglespeciesnonlineardiffusionsystemwithrandomperturbation