一类三维三次系统极限环的新下界  

New Lower Bounds of Limit Cycles for a Class of Three-dimensional Cubic Systems

作　　者：刘桔坤 黄文韬 刘宏普 LIU Jukun;HUANG Wentao;LIU Hongpu(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin Guangxi 541004,China;School of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2022年第6期109-115,共7页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12061016);广西科技基地和人才专项(桂科AD21220114)。

摘　　要：研究一类具有2个对称奇点的三维三次系统的中心和极限环分支问题。首先借助计算机代数软件计算其伴随复系统的前8阶奇点量,得到这2个奇点成为中心的一组必要条件,并进一步证明其充分性;然后导出这2个奇点同时成为8阶细焦点的条件;最后利用雅可比行列式证明系统至少存在16个小振幅极限环,并给出三维三次系统极限环个数的一个新的下界。The center and limit cycle bifurcation of a class of three-dimensional cubic systems with two symmetric singularities are studied.Firstly,the first eight singular points of the adjoint complex system are calculated with the help of computer algebra software,a set of necessary conditions for the two singular points to become the center are obtained,and its sufficiency is further proved.Then the condition that the two singularities become the 8th order fine focus at the same time is derived.Finally,by using the Jacobian determinant method,it is proved that there are at least 16 small amplitude limit cycles in the system,and a new lower bound for the number of limit cycles of three-dimensional cubic system is given.

关 键 词：三维三次系统 奇点量 中心流形 中心 极限环 

分 类 号：O175.12[理学—数学]