摘要
利用奇点理论分析了平衡点的性态,借助Dulac函数法讨论了闭轨的不存在性,利用Hopf分支理论分析得到极限环存在性的若干充分条件,并利用Л.А.Чеpkac和Л.И.Ж.илeвыч唯一性定理分析得到极限环唯一性和稳定性的若干充分条件.
The properties of equilibrium points are analyzed by the singular point theory,and the non-existence of closed orbit is discussed in view of Dulac function.By using Hopf bifurcation theory,some sufficient conditions for the existence of limit cycles are obtained.Furthermore,with the theorem Л.А.Чеpkac and Л.И.Ж.илeвыч,some sufficient conditions for the uniqueness and stability for limit cycles of such systems are obtained.
出处
《吉首大学学报（自然科学版）》
CAS
2010年第4期18-23,共6页
Journal of Jishou University(Natural Sciences Edition)
基金
成都信息工程学院自然科学与技术发展基金资助项目(CSRF200601)
关键词
平面系统
极限环
存在性
唯一性
planar system
limit cycle
existence
uniqueness
