一类五次代数曲线的图形分类  

Graph Classification for a Class of Quintic Algebra Curves

作　　者：王全迪[1] 张金焕[1] 

机构地区：[1]华南理工大学数学科学学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2006年第11期109-113,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571063)

摘　　要：用平面动力系统定性分析方法和数学软件Mathematica对五次代数曲线的图形进行分类.首先建立一个与这类代数曲线相对应的平面动力系统,然后研究奇点的分布及性质,找出参数平面的分支曲线,再用Mathematica画出了代数曲线的图形,并完成了图形的分类,将这一类代数曲线的图分为了12类.The graph classification for a class of quintic algebra curves is carried out by means of the software Mathematica and the qualitative analysis method of planar dynamical system. In the classification, first, a planar dynamical system corresponding to the quintic algebra curves is constructed. Next, the distributions and properties of singular points are studied. Then, the bifurcation curves are given on the parametric plane. Finally, the graphs of the algebral curves are drawn by using the software Mathematica. Thus, the classification is completed, dividing the graphs into twelve types.

关 键 词：五次代数曲线 数学模型 图形分类 平面动力系统 定性分析 数学软件 

分 类 号：O175.12[理学—数学]