一类具有比率依赖型功能反应和Allee效应的Leslie-Gower捕食者-食饵模型的 Hopf分支

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一类具有比率依赖型功能反应和Allee效应的Leslie-Gower捕食者-食饵模型的 Hopf分支
Hopf Bifurcation of a Leslie-Gower with Ratio-Dependent Functional Response and Allee Effect

DOI: 10.12677/PM.2022.127125, PDF, 下载: 264 浏览: 434
作者: 贾昕蓺：西北师范大学数学与统计学院，甘肃兰州
关键词: Leslie-Gower模型；比率依赖型功能反应；平衡点；稳定性；Hopf分支；Leslie-Gower Model； Ratio-Dependent Functional Response； Equilibrium Points； Stability； Hopf Bifurcation

摘要: 本文研究带比率依赖型的功能反应和Allee效应的Leslie-Gower捕食者-食饵模型的稳定性与Hopf分支。首先讨论平衡点的局部渐近稳定性，然后以捕食者的内在增长率 s为分支参数，给出 Hopf 分支存在的条件。最后，利用规范型理论和中心流形定理分析 Hopf 分支的方向及分支周期解的稳定性。

Abstract: In this paper, we investigate the stability and Hopf bifurcation of a Leslie-Gower predator-prey model with Ratio-Dependent Functional Response and Allee effect. First, the local asymptotic stability of the equilibrium points is discussed, and then the condition of the existence of Hopf bifurcation is given by taking the ratio s of the intrinsic growth rate for the predator as the bifurcation parameter. Finally, using the canonical theory and the central manifold theorem, the direction of Hopf bifurcation and the stability of periodic solution of bifurcation are analyzed.

文章引用：贾昕蓺. 一类具有比率依赖型功能反应和Allee效应的Leslie-Gower捕食者-食饵模型的 Hopf分支[J]. 理论数学, 2022, 12(7): 1136-1145. https://doi.org/10.12677/PM.2022.127125

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