摘要
关于平面自治微分系统的定性研究,2次系统已有大量系统的结果,但是还没有得到完全解决,随着2次系统大量研究成果的产生,对3次系统研究工作也日益增多。文章对一类(2n+1)次微分系统进行了详细的讨论,主要运用G.Sansone定理及旋转向量场理论分析得出其极限环的存在性与惟一性及闭轨的完整结果,这是对3次系统研究成果的推广和延伸。3次系统的某些结论,在本文成为当n=1时的自然结论。
This paper considers the （2n＋1）th differential systems. G. Sansone theorem and the theory of rotated vector fields are applied to discuss the existence and uniqueness of limit cycles for the planar differential systems. The existence, uniqueness and closed orbit of limit cycles are obtained, which are the extension of the results of the third differential system. Some results of the third differential system are the certain results as n=1.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第4期588-590,共3页
Journal of Hefei University of Technology：Natural Science
关键词
平面微分系统
极限环
存在与惟一性
闭轨
planar differential system
limit cycle
existence and uniqueness
closed orbit
