This paper investigates the qualitative properties near a degenerate fixed point of a discrete predator–prey model with cooperative hunting derived from the Lotka–Volterra model where the eigenvalues of the corresponding linear operator are ±1. Applying the theory of the normal form and the Takens's theorem, we change the problem of this discrete model into the one of an ordinary differential system. With the technique of desingularization to blow up the degenerate equilibrium of the ordinary differential system, we obtain its qualitative properties. Utilizing the conjugacy between the discrete model and the time-one mapping of the vector field, we obtain the qualitative structures of this discrete model.

中文翻译：

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具有协同狩猎的离散捕食者-猎物模型退化不动点的定性分析

本文研究了具有合作狩猎的离散捕食者-猎物模型的退化不动点附近的定性属性，该模型源自 Lotka-Volterra 模型，其中相应线性算子的特征值为 ±1。应用范式理论和Takens定理，我们把这个离散模型的问题转化为一个普通微分系统的问题。用去奇异化技术打破普通微分系统的退化平衡，我们得到了它的定性性质。利用离散模型与向量场的时间一映射之间的共轭性，我们获得了该离散模型的定性结构。