具有恐惧效应的Leslie-Gower捕食-食饵模型的Hopf分支

doi:10.13438/j.cnki.jdzk.2026.02.003

吉首大学学报（自然科学版） ›› 2026, Vol. 47 ›› Issue (2): 10-17.DOI: 10.13438/j.cnki.jdzk.2026.02.003

具有恐惧效应的Leslie-Gower捕食-食饵模型的Hopf分支

范茹,李杰梅

(兰州交通大学数理学院,甘肃兰州 730070)

出版日期:2026-03-25 发布日期:2026-04-24
作者简介:范茹(2001—),女,河南新乡人，兰州交通大学数理学院硕士研究生,主要从事生物数学研究
基金资助:
甘肃省自然科学基金重点资助项目(23JRRA861)

Hopf Bifurcation of the Leslie-Gower Predator-Prey Model with Fear Effect

FAN Ru,LI Jiemei

(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

Online:2026-03-25 Published:2026-04-24

摘要/Abstract

摘要：研究了一类具有Holling-Ⅱ型功能性反应函数和恐惧效应的Leslie-Gower捕食-食饵模型的Hopf分支性态.运用Hurwitz判据分析了模型平衡点的存在性和稳定性,并通过分支理论选取恐惧程度作为分支参数,严格证明了模型在一定条件下会产生Hopf分支.在此基础上,进一步探讨了Hopf分支的方向、周期解的稳定性和极限环的存在性,完整刻画了恐惧效应下模型的复杂动力学行为.

关键词： Leslie-Gower, Hopf分支, 恐惧效应, Poincaré-Andronov-Hopf分支定理

Abstract: We investigate the Hopf bifurcation behavior of a Leslie-Gower predator-prey model with Holling-type Ⅱ functional response and fear effect.By applying the Hurwitz criterion,we analyze the existence and stability of the equilibrium points of the model.Taking the fear factor as the bifurcation parameter and combining with bifurcation theory,we rigorously prove that the model undergoes a Hopf bifurcation under certain conditions.On this basis,we further discuss the direction of the Hopf bifurcation,the stability of the periodic solutions,and the existence of limit cycles,and completely characterize the complex dynamical behaviors of the model under the fear effect.

Key words: Leslie-Gower model, Hopf bifurcation, fear effect, Poincaré-Andronov-Hopf Bifurcation Theorem

范茹, 李杰梅. 具有恐惧效应的Leslie-Gower捕食-食饵模型的Hopf分支[J]. 吉首大学学报（自然科学版）, 2026, 47(2): 10-17.

FAN Ru, LI Jiemei. Hopf Bifurcation of the Leslie-Gower Predator-Prey Model with Fear Effect[J]. Journal of Jishou University(Natural Sciences Edition), 2026, 47(2): 10-17.

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具有恐惧效应的Leslie-Gower捕食-食饵模型的Hopf分支

Hopf Bifurcation of the Leslie-Gower Predator-Prey Model with Fear Effect

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