一类2n+1次多项式系统的焦点量及极限环的唯一性  

The decision of center and focus and uniqueness of limit cycles of a(2n+1)-th polynomial system

作　　者：谢向东 薛亚龙 许丽莉 XIE Xiang-dong;XUE Ya-long;XU Li-li(College of Mathematics and Physics,Ningde Normal University,Ningde,Fujian 352100,China)

机构地区：[1]宁德师范学院数理学院,福建宁德352100

出　　处：《宁德师范学院学报（自然科学版）》2022年第2期113-115,139,共4页Journal of Ningde Normal University(Natural Science)

基　　金：福建省教育厅中青年科研项目(JAT200690,JT190602).

摘　　要：研究2n+1次多项式系统dx/dt=-y+δx+a_(2)xy+a_(5)xy^(2),dy/dt=x(1+by^(2n)),给出系统的焦点量(或奇点量)W_(0)=δ,W_(1)=a_(5).证明W_(0)W_(1)≥0时,O(0,0)外围不存在极限环;而当W_(0)W_(1)<0时,O(0,0)外围至多一个极限环.To study the uniqueness of limit cycles for a class of(2n+1)-th Polynomial system dx/dt=-y+δx+a_(2)xy+a_(5)xy^(2),dy/dt=x(1+by^(2n)),and the focus quantity W_(0)=δ,W_(1)=a_(5)of the system is obtained.It is proved that if W_(0)W_(1)≥0,the system has no limit cycles;if W_(0)W_(1)<0,the system has at most one limit cycle.

关 键 词：2n+1次多项式系统 极限环 焦点量 

分 类 号：O175[理学—数学]