Stochastic permanence, stationary distribution and extinction of a single-species nonlinear diffusion system with random perturbation

Li Zu; Daqing Jiang; Donal O'Regan

doi:10.13025/26496

Stochastic permanence, stationary distribution and extinction of a single-species nonlinear diffusion system with random perturbation

Li Zu
, Daqing Jiang
, Donal O'Regan

Mathematics

Changchun University
Northeast Normal University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

14 Citations (Scopus)

Abstract

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.

Original language	English
Article number	320460
Journal	Abstract and Applied Analysis
Volume	2014
DOIs	https://doi.org/10.13025/26496 https://doi.org/10.1155/2014/320460
Publication status	Published - 2014

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10.13025/26496Licence: CC BY-NC-ND
10.1155/2014/320460

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title = "Stochastic permanence, stationary distribution and extinction of a single-species nonlinear diffusion system with random perturbation",

abstract = "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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AU - Zu, Li

AU - Jiang, Daqing

AU - O'Regan, Donal

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10379/14541

UR - https://www.scopus.com/pages/publications/84893725271

U2 - 10.13025/26496

DO - 10.13025/26496

M3 - Article

SN - 1085-3375

VL - 2014

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

M1 - 320460

ER -

Stochastic permanence, stationary distribution and extinction of a single-species nonlinear diffusion system with random perturbation

Abstract

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