具有三个极限环的四维等位基因选择迁移模型  

A four dimensional allele selective migration model with three limit cycles

作　　者：郭立欣 历智明 GUO Lixin;LI Zhiming(School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2024年第2期218-233,共16页Pure and Applied Mathematics

基　　金：国家自然科学基金(12271432)。

摘　　要：本文主要研究了四维等位基因选择迁移模型.根据Liapunov稳定性定理, Hopf分支理论和中心流形定理,借助Maple计算中心焦点量La的程序Liapunov常数得到了两个稳定的极限环,又得到该系统属于Zeeman分类的第27类,然后根据Poincar′e-Bendixson环域定理得到了一个不稳定的极限环,进而推导出了四维等位基因选择迁移模型存在三个极限环.In this paper, we mainly studied the four-dimensional allelic selection transfer model. According to Liapunov stability theorem, Hopf bifurcation theory, and central manifold theorem, two stable limit cycles are obtained by using Maple's program Liapunov constant to calculate the central focus quantity La, and it is concluded that the system belongs to the Zeeman class 27. Then an unstable limit cycle is obtained according to Poincar′e-Bendixson ring field theorem, and then it is deduced that there are three limit cycles in the four-dimensional allele selection transfer model.

关 键 词：极限环 等位基因 选择迁移模型 中心流形定理 

分 类 号：O19[理学—数学]