一类Holling-III型的合作捕食者-食饵模型的Hopf分支研究
Hopf Bifurcation Analysis of a Holling-III Cooperation Predator-Prey Model
DOI: 10.12677/AAM.2021.105165, PDF, 下载: 260  浏览: 494 
作者: 阮 虎：西北师范大学数学与统计学院，甘肃 兰州
关键词: 合作模型；Holling-III 型功能反应；平衡点；稳定性；Hopf 分支；Cooperation Model； Holling-III Functional Response； Equilibrium Points； Stability； Hopf Bifurcation
摘要: 本文研究带 Holling-III 型功能反应合作捕食者-食饵模型的稳定性与 Hopf 分支. 利用线性化分析和分支理论, 首先, 讨论平衡点的存在性及唯一正平衡点的局部渐近稳定性, 然后以 α∗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 cooperation predator-prey model with Holling-III. Using the linearization analysis and bifurca- tion theory, firstly, the existence of the equilibrium and the local asymptotic stability of the unique positive equilibrium points are discussed, and then the condition of the existence of Hopf bifurcation is given by taking the α∗ 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：阮虎. 一类Holling-III型的合作捕食者-食饵模型的Hopf分支研究[J]. 应用数学进展, 2021, 10(5): 1550-1558. https://doi.org/10.12677/AAM.2021.105165

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