%0 Journal Article
%T 带有合作捕猎Holling III型的捕食者-食饵模型<br>A Predator-Prey Model of Collaborative Hunting with Holling III Type
%A 闻韬
%J Advances in Applied Mathematics
%P 3709-3727
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.128366
%X 本文研究了带有强弱Allee效应，合作捕猎和反捕食行为的捕食者-食饵模型的动力学行为。我们进 行了详细的平衡点存在性和稳定性分析, 分析了鞍结分支，Hopf分支和余维二极限环的尖点，并通过数值模拟来验证理论结果，得到极限环的余维二尖点的存在性，进而得到系统至少存在三个 共存的极限环，表明在合作捕猎的影响下，具有Allee效应和反捕食行为的捕食者-食饵模型的动力学行为会更加复杂。<br />
This paper investigates the dynamic behavior of a predator-prey model with strong and weak Allee effects, cooperative hunting, and anti-predator behavior. We discuss the existence and stability of the equilibrium points, and we perform a detailed bifurcation analysis including the saddle-node bifurcation, Hopf bifurcation and codimension-2 cusp of limit cycle, then we verified the theoretical results through numerical simula- tion, obtained the existence of the codimension- 2 cusp of the Limit cycle, and then obtained that the system has at least three coexisting Limit cycles, indicating that under the influence of cooperative hunting, the dynamic behavior of the predator-prey model with Allee effect and anti-predator behavior will be more complex.
%K 合作捕猎，Allee效应，Hopf分支，捕食者-食饵模型，鞍结分支，余维二极限环的尖点<br>Cooperative Hunting
%K Allee Effect
%K Hopf Bifurcation
%K Predator-Prey Model
%K Saddle-Node Bifurcation
%K Codimension-2 Cusp of Limit Cycle
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=71148