一类修改的Leslie-Gower型随机模型的性质分析  

Properties analysis of a class of stochastic modified Leslie-Gower model

作　　者：于子倩 刘铭[1] 徐晓峰 YU Ziqian;LIU Ming;XU Xiaofeng(School of Science,Northeast Forestry University,Harbin 150040,China;School of Mathematical Science,Heilongjiang University,Harbin 150080,China)

机构地区：[1]东北林业大学理学院,哈尔滨150040 [2]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2020年第3期260-271,共12页Journal of Natural Science of Heilongjiang University

基　　金：教育部高校基本科研业务费专项资金资助项目(2572016CB08)。

摘　　要：考虑随机因素的影响,研究了一类具有白噪声扰动的随机捕食-被捕食模型。首先通过构造适当的Lyapunov函数,应用Ito公式以及随机微分方程的比较定理等方法,得到了系统全局正解的存在性;其次,研究了系统具有持久性和灭绝性的条件,并讨论了系统的平稳分布以及遍历性;最终给出了相应的数值模拟,验证了得到的结论。A stochastic predator-prey model with white noise perturbation is investigated by considering the influence of random factors. Firstly, by constructing the appropriate Lyapunov function and applying the Ito formula and the comparison theorem of stochastic differential equations, the existence of the global positive solution is obtained. Secondly, the conditions of the persistence and extinction of the system are given, and the stationary distribution and ergodicity of the system are discussed. Finally, some numerical simulations are presented to verify the obtained conclusions.

关 键 词：随机捕食-被捕食模型 V函数 ITO公式 持久性 平稳分布 遍历性 

分 类 号：O175.1[理学—数学]