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Stochastic permanence, stationary distribution and extinction of a single-species nonlinear diffusion system with random perturbation. (English) Zbl 1406.92546

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.

MSC:

92D25 Population dynamics (general)
92D40 Ecology
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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