一类平面五次向量场的奇点分岔  

Singular Point Bifurcation of a Class of Five-Degree Plane Vector Fields

作　　者：程雪梅[1] 

机构地区：[1]潍坊学院,山东潍坊261061

出　　处：《潍坊学院学报》2010年第2期73-75,共3页Journal of Weifang University

摘　　要：为了完整全面的了解平面多项式系统的结构稳定性问题,分岔现象的研究显得尤为重要。五次向量场的分岔现象由于次数的增加而变得复杂,利用Liapunov-Schmidt方法可以将奇点附近的分岔情况进行简化处理,即给出一类平面五次向量场在原点附近的奇点分岔分析。为进一步讨论系统的全局分岔现象提供基础条件。In order to fully comprehensive understanding of the structure stability issues of the plane polynomial system,the study of bifurcation phenomena is important.Five-degree vector field bifurcation is complicated due to increasing of the degree number.Using the Liapunov-Schmidt method,singularites bifurctios in the vicinity of condition should be simplified.That is,the singular point bifurcation analysis is given of a class of five-degree plane vector fields in the vicinity.For further discussion global bifurcations of the system provides the basis.

关 键 词：五次向量场 奇点分岔 扰动 

分 类 号：O175.12[理学—数学]