一类高次多项式系统的定性分析  

Qualitative analysis for a class of odd polynomial differential system

作　　者：蒋自国[1,2] 

机构地区：[1]四川大学数学学院,成都610064 [2]阿坝师范高等专科学校数学系,汶川623000

出　　处：《四川大学学报（自然科学版）》2008年第6期1293-1298,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省教育厅自然科学基金(2006C056)

摘　　要：作者研究了一类平面高次多项式微分系统的奇点性态和极限环问题,给出了系统的奇点为稳定焦点、不稳定焦点和鞍点的充分条件.通过选取恰当的Dulac函数,作者给出了该系统极限环不存在的一些充分条件,并利用Hopf分支问题的Liapunov第二方法得到了该系统极限环存在性和稳定性的若干充分条件,然后利用Cherkas和Zheilevych的唯一性定理得到了极限环唯一性的若干充分条件.The type of singular point and the limit cycle problem for a class of odd polynomial system is studied. Some sufficient conditions for the type of singular point of such system are obtained. By making a Dulac function, some sufficient conditions for non-existence of limit cycle of such system are obtained. By using the second method of Liapunov of Hopf problem, some sufficient conditions for the existence and stability of limit cycles of such system are obtained. Furthermore, by applying Cherkas and Zheilevych＇ s theorem about uniqueness, some sufficient conditions for the uniqueness of limit cycles of such system are obtained.

关 键 词：多项式系统 奇点 极限环 存在性 唯一性 

分 类 号：O175.12[理学—数学]