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. © 2014 Li Zu et al.