空间向量场中一类微分系统无穷远点的极限环分支  

Limit cycles bifurcation at infinity of a class of differential system in space vector fields

作　　者：刘灿辉 杜超雄 LIU Canhui;DU Chaoxiong(School of Mathematics, Changsha Normal University, Changsha 410100, China)

机构地区：[1]长沙师范学院数学科学学院,湖南长沙410100

出　　处：《邵阳学院学报（自然科学版）》2021年第3期13-22,共10页Journal of Shaoyang University：Natural Science Edition

基　　金：湖南省教育厅重点项目(18A525);湖南省自然科学基金(2020JJ4630)。

摘　　要：对空间向量场中一类五次微分多项式系统的极限环分支问题进行研究。通过进行两个合适的变换并使用奇点量的方法在正定的中心流形下对无穷远点的广义李雅普诺夫常数即广义焦点量进行计算和化简,得出了该系统的无穷远点存在五阶广义焦点量;进一步讨论了其无穷远点极限环分支问题,得出该系统在一定的扰动下可以同时分支出5个大振幅极限环的结论。The bifurcation of limit cycles for a class of quintic differential polynomial systems in space vector fields was studied.By making two suitable transformations and using the method of singular point quantity,the generalized Lyapunov Constant(i.e.the generalized focus quantity)at infinity was calculated and simplified in a positive definite central manifold.It was found that there was a fifth order generalized focus quantity at infinity of the system.Furthermore,the bifurcation problem of limit cycle at infinity was discussed.It was concluded that the system could be divided simultaneously under certain disturbance.The conclusion of five large amplitude limit cycles was drawn.

关 键 词：空间向量场 广义焦点量 中心流形 极限环分支 

分 类 号：O175[理学—数学]