一类具退化承载力捕食者–食饵模型的Hopf分支
Hopf Bifurcation of a Predator-Prey Model with Degenerate Carrying Capacity
DOI: 10.12677/PM.2022.121009, PDF,   
作者: 王碧君：西北师范大学数学与统计学院，甘肃 兰州
关键词: 退化承载力；平衡点；稳定性；Hopf分支；Degradation Capacity； Equilibrium Point； Stability； Hopf Bifurcation
摘要: 本文研究带Holling-II型功能反应的具有退化承载能力的捕食者–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，然后以退化系数ρ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 study the stability and the Hopf bifurcation of apredator-prey model with degenerate carrying capacity with Holling-II type of functional response. Firstly, the local asymptotic stability of the equilibrium point is discussed. Then, the existence condition of the Hopf bifurcation is given by taking the degradation coefficient ρ as the branching parameter. Finally, the direction of the Hopf bifurcation and the stability of its periodic solution are analyzed by means of canonical theory and central manifold theorem.
文章引用：王碧君. 一类具退化承载力捕食者–食饵模型的Hopf分支[J]. 理论数学, 2022, 12(1): 62-70. https://doi.org/10.12677/PM.2022.121009

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