Allee效应下的一类捕食-食饵系统的动力分析  

Dynamic Analysis of a Predator-Prey System with the Allee Effect

作　　者：岳宗敏 王娇 卢琨 YUE Zong-min;WANG Jiao;LU Kun(School of Arts and Sciences,Shaanxi University of Science and Technology,Xi’an,710021,China)

机构地区：[1]陕西科技大学文理学院数学系

出　　处：《数学的实践与认识》2019年第22期274-283,共10页Mathematics in Practice and Theory

基　　金：陕西省教育厅专项(14JK1081);榆林市2018年科学研究与开发项目(2018-2-40)

摘　　要：建立了一个食饵具有一个保护的区域和非保护区域的捕食-食饵模型,在考虑环境制约的情况下,同时考虑了保护区的食饵具有Allee效应.根据食饵与捕食者的生物意义以及一些参数的快慢两个时间尺度,将系统分为快速系统和慢速系统.通过动力分析,给出了慢速系统平衡点的存在性、全局稳定性、Hopf分支以及极限环存在的条件,并通过数值分析及数值模拟加以验证结果表明,Allee效应的存在改变了两物种的共存的条件,使系统动力行为更为复杂.In this paper we establish a predator-prey model with a protection area and a open habitat for prey.The Allee effect in the prey of protection area and the environment carrying capacity of prey are considered.Accor-ding to the biology of predator-prey system,fast and slow time scales are considered in some of the parameters.Based on two different time scales,the system is divided into a fast and a slow system.We analyze the dynamics of the slow system.Existence and global stability of equilibriums,existence of Hopf bifurcation and the limit cycle are performed.Combining mathematica analysis and numerical simulation,we verified the results above.The results show that the Allee effect change the conditions of the two species coexist.It makes the system dynamic behavior more complicated.

关 键 词：捕食-食饵模型 ALLEE效应 快慢系统 全局稳定性 HOPF分支 

分 类 号：O17[理学—数学]