文章基本信息

标题：Dynamical analysis of a ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting in a random environment
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作者：Guijie Lan ; Yingjie Fu ; Chunjin Wei 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：198
DOI：10.1186/s13662-018-1625-8
语种：English
出版社：Hindawi Publishing Corporation
摘要：The objective of this paper is to study the dynamics of the stochastic ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting. For the autonomous system, sufficient conditions for globally positive solution and stochastic permanence are established. Then, applying comparison theorem for stochastic differential equation, sufficient conditions for extinction and persistence in the mean are obtained. In addition, we prove that there exists a unique stationary distribution and it has ergodicity under certain parametric restrictions. For the periodic system, we obtain conditions for the existence of a nontrivial positive periodic solution. Finally, numerical simulations are carried out to substantiate the analytical results.
关键词：Predator–prey system ; Harvesting ; Stochastic permanence ; Stationary distribution and ergodicity ; Positive periodic solution