具有十二个大振幅极限环的七次多项式系统  

A class of seventh-degree polynomial system with twelve large-amplitude limit cycles

作　　者：吴海涛[1] 黄文韬[1] 梁德辉[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《兰州大学学报（自然科学版）》2009年第4期121-126,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(10871206);广西省自然科学基金项目(0575092)

摘　　要：研究一类七次多项式微分系统无穷远点的极限环分支问题.首先将该问题转换成在原点的极限环分支问题,然后通过奇点量的计算,推导出系统原点(对应无穷远点)的中心条件以及最高阶细焦点的条件,给出了七次多项式系统可在无穷远点分支出12个极限环的实例.Bifurcation of limit cycles at infinity for a class of seven-degree polynomial system is studied, in which the problem for bifurcation of limit cycles at infinity is transferred into that at the origin. By the computation of singular point values, the conditions of the origin （correspondingly infinity） to be a center and the highest degree fine focus are derived. Finally, it is showed firstly that a seventh-degree differential system which allows the appearance of twelve limit cycles in a small enough neighborhood of infinity is constructed.

关 键 词：七次多项式微分系统 无穷远点 奇点量 中心条件 极限环分支 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]