一类平面五次系统的极限环的存在唯一性  

The Existence Uniqueness of Limit Cycles for a Class of Plane Five-Degree System

作　　者：刘兴国[1] 黄立宏[2] 

机构地区：[1]湖南工业大学信息与计算科学系,湖南株洲412008 [2]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《湖南工业大学学报》2007年第3期21-26,共6页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(10371034);国家博士点专项科研基金资助项目(20050532023)

摘　　要：研究一类平面五次多项式系统,利用基于Poincaré思想的形式级数法进行了中心焦点的判定,借助Dulac函数法讨论了闭轨的不存性,利用Hopf分支理论分析建立从平衡点分支出极限环的若干充分条件,利用Л.А.Черкас和Л.И.Жилевыч的唯一性定理分析得到了极限环唯一性与稳定性的若干充分条件。Abstract： Studying on a class of planar quintic polynomial systems, the center and focus are judged by the formal series method. then by the Dulac function, the non-existence of closed orbit is discussed. And after Hopf bifurcation theory, some sufficient conditions for the existence of limit cycles of such systems are also obtained. Furthermore, with the theorem of Л.А.Черкасand Л.ИЖилевыч, some sufficient conditions for the uniqueness and stability of limit cycles of such systems are established.

关 键 词：中心 焦点 极限环 存在性 唯一性 

分 类 号：O175.12[理学—数学]