一个离散捕食模型退化不动点的稳定性

Stability of Degenerate Fixed Point for a Discrete Predator-prey Model

研究了一个具有Allee效应的离散捕食模型退化不动点的稳定性.首先计算模型的正规形,应用Picard迭代和Takens’s定理将正规形嵌入向量场的流.然后通过极坐标变换得到了向量场退化平衡点的稳定性.最后利用向量场与模型的近似关系得到退化不动点的稳定性.

In this paper,we study the stability of the degenerate fixed point for a discrete predator-prey model with Allee effect.Firstly,the normal form of the model is calculated,and the normal form is embed-ded into the flow of a vector field by using Picard iteration and Takens's theorem.Then the stability of the degenerate equilibrium point of vector field is obtained by polar coordinate transformation.Finally,the sta-bility of the degenerate fixed point is obtained by using the approximate relation between the vector field and the model.