一类2n+1次多项式微分系统的局部极限环分支  

Bifurcations of local limit cycles for a class of 2n+1 degree polynomial differential system

作　　者：徐慧栩[1] 黄文韬[1] 张理[2] 

机构地区：[1]桂林电子科技大学计算科学与数学系,广西桂林541004 [2]安微工业大学数理学院,安微马鞍山243002

出　　处：《纯粹数学与应用数学》2006年第4期549-555,共7页Pure and Applied Mathematics

基　　金：国家自然科学基金资助项目(60464001);广西自然科学基金资助项目(0575092)

摘　　要：研究了一类2n+1次多项式微分系统在原点的局部极限环分支问题,通过计算与理论推导得出了该系统原点的奇点量表达式,确定了系统原点的中心条件以及最高阶细焦点的条件,并在此基础上构造出系统在原点分支出4个极限环的实例.The bifurcations of local limit cycles at the origin for a class of 2n＋ 1 degree polynomial differential system are investigated. By computation and deducing theo-ries,the expressions of singular points of the system at the origin are obtained. Then the conditions of center and the highest fine focal points are gotten. Finally, an exmple of poly-nomial differential system with four limit cycles bifurcating from the origin is constructed.

关 键 词：高次奇点 焦点量 奇点量 极限环分支 

分 类 号：O175.12[理学—数学]