| 一类具有Z3等变性质的四次哈密尔顿向量场相图研究 |
| |
| 引用本文： | 黄益,吴玉海.一类具有Z3等变性质的四次哈密尔顿向量场相图研究[J].甘肃联合大学学报(自然科学版),2011,25(6):5-10. |
| |
| 作者姓名： | 黄益 吴玉海 |
| |
| 作者单位： | 江苏大学理学院,江苏镇江,212012 |
| |
| 基金项目： | 江苏大学本科生科研计划项目 |
| |
| 摘 要： | 本文利用微分方程的定性理论及分支方法,分析了一类具有Z3等变性质的平面四次哈密尔顿向量场有限远奇点及无穷远奇点个数及其类型与参数关系,给出该向量场的分支图,并根据系统等变性给出了在参数空间里所有可能的相图.在文章最后部分运用数学软件演示了当一个参数固定,另一个参数连续变化时向量场相图变化的情况.
|
| 关 键 词： | 哈密尔顿向量场 奇点 相图 分支图 |
Study on the Phase Portraits of a Class of Quartic Z3-equivariant Hamiltonian Vector Field |
| |
| HUANG Yi,WU Yu-hai.Study on the Phase Portraits of a Class of Quartic Z3-equivariant Hamiltonian Vector Field[J].Journal of Gansu Lianhe University :Natural Sciences,2011,25(6):5-10. |
| |
| Authors: | HUANG Yi WU Yu-hai |
| |
| Institution: | HUANG Yi,WU Yu-hai (Department of Mathematics and Institute of Sciences,Jiangsu University,Zhenjiang 212012,China) |
| |
| Abstract: | In this paper,differential qualitative analysis method is applied to study the number and typies of finite singularities and infinite singularities of one class of Z3 equivalent planar quartic Hamiltonian vector field having two parameters.Bifurcation diagram and phase portraits of vector field are given.In the final part of the paper,variations of phase portraits of vector field are illustrated as parameter changes by using mathematical software. |
| |
| Keywords: | hamiltonian vector field singularity phase portraits bifurcation diagram |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
