一类带恐惧效应的 Holling-Tanner 模型的Hopf 分支
Hopf Bifurcation of a Holling-TannerModel with Fear Effect
DOI: 10.12677/PM.2023.135135, PDF, HTML, 下载: 146  浏览: 258 
作者: 赵 倩：西北师范大学，数学与统计学院，甘肃 兰州
关键词: Holling-Tanner 模型；恐惧效应；平衡点；稳定性；Hopf 分支；Holling-Tanner Model； Fear Effect； Equilibrium Points； Stability； Hopf Bifurcation
摘要: 本文采用包含猎物避难所的 Holling-Tanner 捕食者-食饵模型研究了由于捕食者的恐惧而导致的反捕食者行为的影响。首先讨论平衡点的局部渐近稳定性，然后以捕食者的恐惧水平 k 为分支参数，给出 Hopf 分支存在的条件。最后，利用规范型理论，Poincae´-Andronov-Hopf 分支定理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。 通过计算分析，发现恐惧效应可以降低捕食者在正平衡状态下的种群密度。
Abstract: In this paper, we investigate the influence of anti-predator behaviour due to the fear of predators with a Holling-Tanner preydator-prey model incorporating a prey refuge. 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 fear level k of 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. Through calculation and analysis, it is found that the fear effect can reduce the population density of predator at the positive equilibrium.
文章引用：赵倩. 一类带恐惧效应的 Holling-Tanner 模型的Hopf 分支[J]. 理论数学, 2023, 13(5): 1321-1332. https://doi.org/10.12677/PM.2023.135135

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