Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation-Reference-Cited by-同舟云学术

Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation

Published:2014 Issue: Volume:2014 Page:1-14
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Zu Li¹²,Jiang Daqing²,O’Regan Donal³

Affiliation:

1. School of Science, Changchun University, Changchun 130022, China

2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Abstract

We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion amongnpatches. 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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/320460.pdf

Reference17 articles.

1. Persistence and extinction in single-species reaction-diffusion models

2. Global asymptotic behavior in single-species discrete diffusion systems

3. Global stability and predator dynamics in a model of prey dispersal in a patchy environment