具有恐惧效应和Holling Ⅱ类功能性反应捕食-食饵斑块模型的研究  

Study of a Predator-Prey Patchy Model with Fear Effect and Holling Ⅱ Functional Response

作　　者：陈丽娟[1] 朱紫睿 夏越 CHEN Lijuan;ZHU Zirui;XIA Yue(School of Mathematics and Statistics,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《应用数学》2024年第4期893-902,共10页Mathematica Applicata

基　　金：福建省自然科学基金资助项目(2021J01614)。

摘　　要：本文提出食饵具有恐惧效应和Holling Ⅱ类功能性反应的捕食-食饵斑块模型,讨论平衡点的存在性和稳定性.并进一步得到边界平衡点的全局稳定性.我们发现,随着恐惧效应因子的增加,系统唯一正平衡点的稳定性会发生变化.因此,在适当条件下,系统会在唯一的正平衡点附近产生Hopf分支现象.数值模拟验证了所得理论结果的正确性.In this paper,we propose a predator-prey patchy model with fear effect and Holling Ⅱ functional response.The existence and local stability of the equilibria are discussed.Moreover,the global stability of the boundary equilibrium is investigated.Furthermore,we find that with the increase of fear factor,the local stability of the unique positive equilibrium point of the system will change.Therefore,under appropriate condition,Hopf bifurcation will occur at the unique positive equilibrium of the system.Numerical experiments further verify the feasibility of our conclusions.

关 键 词：恐惧效应 扩散 稳定性 HOPF分支 

分 类 号：O626.21[理学—有机化学]