一类三次系统极限环的存在唯一性  

Uniqueness and Existence of Limit Cycle of a Class of Cubic System

作　　者：卜令杰[1] 窦霁虹[1] 刘萌萌[1] 邢伟[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《延安大学学报（自然科学版）》2014年第2期1-5,共5页Journal of Yan'an University：Natural Science Edition

基　　金：陕西省教育厅自然科学专项基金(11JK0511)

摘　　要：研究一类具有二虚不变直线的三次系统,通过对该系统在实平面内的定性分析得出了系统极限环存在性、唯一性的若干充分条件。并将该系统与其相伴系统对比发现,两者无极限环的充分条件相同,但存在唯一极限环的充分条件发生了变化。A class of cubic polynomial differential system with two imaginary invariant line was studied. The qualitative analysis was discussed in the real plane for a class of cubic system, and the conditions for existence and uniqueness of limit cycle were obtained. From the comparison of the polynomial system and it＇s accompany system, we could find that their sufficient conditions of nonexistence limit cycle were the same, but their sufficient conditions of uniqueness of limit cycle had changed.

关 键 词：三次系统 奇点 相伴系统 极限环 

分 类 号：O175.12[理学—数学]