一类平面微分系统的定性分析  

Qualitative Analysis for a Class of Planar Differential Systems

作　　者：刘兴国[1] 吕勇[1] 

机构地区：[1]湖南工业大学理学院,湖南株洲412008

出　　处：《湖南工业大学学报》2008年第4期17-21,共5页Journal of Hunan University of Technology

摘　　要：对一类平面微分系统进行了定性分析: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分支理论分析得到了极限环存在性的若干充分条件,利用Л.А.Черкас和Л.И.Ж.илевыч的唯一性定理分析得到了极限环唯一性和稳定性的若干充分条件。According to the qualitative analysis of a class of planar differential systems, 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. Then after Hopf bifttrcation theory, some sufficient conditions for the existence of limit cycles are obtained. Furthermore, with the theorem of Л.А.Черкас and Л.ИЖилевыч, some sufficient conditions for the uniqueness and stability for limit cycles of such systems are gained.

关 键 词：平面系统 极限环 存在性 唯一性 

分 类 号：O175.12[理学—数学]