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, s...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.227-240-429
Main Authors: Zu, Li, O'Regan, Donal, Jiang, Daqing
Format: Article
Language:English
Subjects:
Applied mathematics
Diffusion
Diffusion processes
Economic models
Endangered & extinct species
Extinction
Growth rate
Logistics
Mathematical research
Mathematics
Noise
Nonlinear theories
Perturbation (Mathematics)
Population
Studies
System theory
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/320460