一类包含恐惧效应的比率依赖型捕食者-食饵模型的 Hopf 分支

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一类包含恐惧效应的比率依赖型捕食者-食饵模型的 Hopf 分支
Hopf Bifurcation of a Rate-Dependent Type Predator-Prey Model with Fear Effects

DOI: 10.12677/PM.2023.137220, PDF, 下载: 162 浏览: 232
作者: 王博：西北师范大学数学与统计学院，甘肃兰州
关键词: 恐惧因子；Michaelis-MIenten 模型；平衡点；稳定性；Hopf 分支；Fear Effect； Michaelis-Menten Model； Equilibrium Points； Stability； Hopf Bifurcation

摘要: 在本文中，研究一类带比率依赖型功能反应的捕食者-食饵模型，模型中考虑了捕食者被线性捕获和食饵对捕食者的反捕食行为。主要讨论食饵恐惧对系统动力学的影响。首先分析平衡点的存在性和稳定性。其次以恐惧因子k 为分支参数，给出 Hopf 分支存在的条件，并且利用中心流形定理分析 Hopf 分支的方向及分支周期解的稳定性。最后，运用 MATLAB 软件进行数值模拟以支持所得结论。

Abstract: In this paper, we investigate the dynamics of a ratio-dependent predator prey model, and considering the linear capture of the predator and the antipredation behavior of a prey toward a predator. Therefore, our aim focuses on the impact of prey fear on the predation system. Firstly, we discuss the local asymptotic stability and the existence of the equilibrium points. Secondly, taking the fear effect k as the bifurcation parameter to give the condition of the existence of Hopf bifurcation, and using the canonical theory and the central manifold theorem to analyze the direction of Hopf bifurcation and the stability of periodic solution of bifurcation. Finally, MATLAB software is used for numerical simulation to support our conclusions.

文章引用：王博. 一类包含恐惧效应的比率依赖型捕食者-食饵模型的 Hopf 分支[J]. 理论数学, 2023, 13(7): 2125-2135. https://doi.org/10.12677/PM.2023.137220

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