摘要
继续相关文献的工作,给出与二次系统Ⅰ相伴的一类三次系统在奇点N(0,1/n)的焦点量公式,证明了系统在细焦点N外围至多有一个极限环,同时证明了当N或O为细焦点时,系统在另一个焦点外围无极限环,结合相关文献的结论,说明了具有细焦点的该系统在全平面至多有一个极限环.
This paper we continue the study of paper [1] and give the focus valus of each order at N(0, 1/n) for a class of accompany system of quadratic differential system I. We have proved that the system has at most one limit cycle surrounding weak focus N,and have proved that if the system (2) has one weak focus, then it has at most one limit cycles surrounding other focus. It means that the system (2) with weak focus has at most one limit cycles in the plane.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第16期208-216,共9页
Mathematics in Practice and Theory
基金
福建省自然科学基金(2010J01010
2008J0185)
福建省科技创新平台计划项目(2009J1007)
关键词
相伴系统
三次系统
细焦点
极限环
唯一性
accompany system
cubic system
weak focus
limit cycle
uniqueness