具有Allee效应、合作狩猎和恒定投放率的Leslie-Gower模型分析
Analysis of a Leslie-Gower model with Alle effects, cooperative hunting, and constant placement rates
AI总结：
本文研究含Allee效应、合作狩猎与恒定投放率的Leslie-Gower模型，分析三重平衡点存在条件，推导不同参数下的平衡点类型，并证明相关分岔现象，丰富了该类模型的动力学理论结果。
摘要：
本文研究了具有Allee效应、合作狩猎和恒定投放率的Leslie-Gower模型的动力学性质。首先分析了该模型三重平衡点的存在条件。随后，运用标准型理论与平面系统定性理论，得出在不同参数条件下，该三重平衡点可以是余维数为2的结点，也可以是余维数为3的平衡点。最后证明了以合作狩猎和投放率为分支参数时，该系统在该结点附近发生余维数为2的分岔。
英文摘要：
This paper investigates the dynamical properties of the Leslie-Gower model with Alle effects, cooperative hunting, and constant placement rates. The conditions for the existence of the triple equilibrium point of the model are first analyzed. Subsequently, the canonical type theory and the qualitative theory of planar systems are applied to obtain that the triple equilibrium point can be a node with a residual dimension of 2 and an equilibrium point with a residual dimension of 3 under different parameter conditions. Finally, it is proved that the system bifurcates with a residual dimension of 2 in the vicinity of the node with cooperative hunting and placement rate as branching parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
