具有捕食者Allee效应的Leslie-Gower模型的动力学分析  

Dynamics of the Leslie-Gower model with Allee effect in predator

作　　者：方侃[1] 曾怀杰 陈晓英[1] FANG Kan;ZENG Huaijie;CHEN Xiaoying(Zhicheng College,Fuzhou University,Fuzhou 350001,China)

机构地区：[1]福州大学至诚学院,福州350001

出　　处：《延边大学学报（自然科学版）》2022年第1期25-29,40,共6页Journal of Yanbian University（Natural Science Edition）

基　　金：福建省自然科学基金面上项目(2019J01651);福建省教育厅中青年项目(JAT191099)。

摘　　要：研究了在Leslie-Gower模型中加入捕食者Allee效应后的模型动力学行为变化.研究表明:加入捕食者Allee效应后,模型的所有正解是一致有界的,唯一的正平衡点是全局渐近稳定的,但两个边界平衡点是不稳定的.Allee效应虽然不会改变正平衡点的稳定性,但其延长了正平衡点趋向稳定状态的时间,同时也改变了原点的性态,即Allee效应不利于系统的稳定性.Dynamic behaviors of the Leslie-Gower model with Allee effect in predator are studied to show the influence of Allee effect.It is shown that positive solutions of this system are all uniformly bounded,and the only positive equilibrium of the system is globally asymptotically stable while the two boundary equilibrium points are all unstable with the Allee effect.The result indicates that Allee effect doesn’t change the stability of the positive equilibrium but makes the system take a longer time to reach its steady-state solution,and it also changes the dynamic behaviors of the original point,which is to say that the Allee effect makes the system become unstable.

关 键 词：Leslie-Gower模型 ALLEE效应 稳定性 捕食者 一致有界 

分 类 号：O175.12[理学—数学]