在线阅读 --自然科学版 2020年5期《一个离散捕食模型退化不动点的稳定性》
一个离散捕食模型退化不动点的稳定性--[在线阅读]
李明山1, 周效良2
1. 南京航空航天大学 理学院, 江苏 南京 211106;
2. 岭南师范学院 数学与统计学院, 广东 湛江 524048
起止页码: 390--394页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.05.004
摘要
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.

Stability of Degenerate Fixed Point for a Discrete Predator-prey Model
LI Mingshan1, ZHOU Xiaoliang2
1. College of Science, Nanjing University of Aeronautics and Astronautics, Jiangsu Nanjing 211106, China;(;
2. School of Mathematics and Statistics, Lingnan Normal University, Guangdong Zhanjiang 524048, China
Abstract:
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 embedded 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 stability of the degenerate fixed point is obtained by using the approximate relation between the vector field and the model.

收稿日期: 2020-02-28
基金项目: 国家自然科学基金(11961021);广东省大学生科技创新培育专项资金资助项目(pdjh2020b0361);南京航空航天大学研究生创新基地开放基金(kfjj20190802)

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