Qualitative analysis of a degenerate fixed point of a discrete predator-prey model with cooperative hunting
Qualitative analysis of a degenerate fixed point of a discrete predator-prey model with cooperative hunting
复制标题
合作狩猎离散捕食者-被捕食模型简并不动点的定性分析
DOI：
10.1002/mma.7468
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发表时间：
2021
影响因子：
2.9
通讯作者：
Deng Shengfu
中科院分区：
文献类型：
--
作者：
Cheng Qi;Zhang Yanlin;Deng Shengfu
研究了一类由Lotka-Volterra模型导出的具有合作捕食的离散捕食模型在退化不动点附近的定性性质，其中相应的线性算子的特征值为±1.应用规范形理论和Takens定理，我们把这个离散模型的问题转化为常微分系统的问题。利用去奇异化技术爆破退化平衡点，得到了该系统的定性性质。利用离散模型和向量场的时间一映射之间的共轭性，我们得到了这个离散模型的定性结构。
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.