• 论文 •

具有Allee效应及非线性扰动的随机单种群模型的平稳分布及灭绝性

1. 山西财贸职业技术学院,太原  030031
• 出版日期:2019-12-25 发布日期:2020-03-20

CHEN Xianli. Stationary Distribution and Extinction of a Stochastic Population Model with Allee Effect and Nonlinear Perturbation[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(12): 2093-2104.

Stationary Distribution and Extinction of a Stochastic Population Model with Allee Effect and Nonlinear Perturbation

Shanxi Vocational and Technical College of Finance and Trade, Taiyuan 030031

• Online:2019-12-25 Published:2020-03-20

This paper investigates the stationary distribution and extinction of a stochastic population model with Allee effect and nonlinear perturbation. The author first proves the existence of global positive solution of the model. Then by constructing a suitable stochastic Lyapunov function, the author establishes sufficient conditions for the existence of an ergodic stationary distribution of the model. Then the author obtains sufficient conditions for extinction of the population in two cases. One is how Allee effect affects extermination of the population and the other is how noises affect extermination of the population. At last, some examples together with numerical simulations are provided to illustrate the analytical results. }

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