| 一类五次代数曲线的图形的定性分析 |
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| 引用本文： | 刘礼文,邱家彩,毛剑峰.一类五次代数曲线的图形的定性分析[J].咸宁学院学报,2007,27(3):23-26. |
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| 作者姓名： | 刘礼文 邱家彩 毛剑峰 |
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| 作者单位： | 1. 咸宁职业技术学院,湖北,咸宁,437100
2. 咸宁学院,数学系,湖北,咸宁,437100 |
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| 摘 要： | 对一类五次代数曲线的结构进行研究．先将其转化为与之对应的平面Hamilton系统，运用平面微分动力系统的定性理论分析的方法，研究其奇点的分布及性质．然后对其系数进行分析、计算，找出其系数参数平面的分支曲线．最后用数学软件Mathematic画出所有可能的平面分支相图，从而把这类代数曲线的相图分成了13类．
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| 关 键 词： | 五次代数曲线 HAMILTON系统 分支曲线 平面相图 定性理论 |
| 文章编号： | 1006-5342（2007）03-0023-04 |
| 修稿时间： | 2006-12-04 |
Qualitative Analysis for a Kind of Five-order Algebra Curve's Graphic |
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| LIU Li-wen,QIU Jia-cai,MAO Jian-feng.Qualitative Analysis for a Kind of Five-order Algebra Curve''''s Graphic[J].Journal of Xianning College,2007,27(3):23-26. |
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| Authors: | LIU Li-wen QIU Jia-cai MAO Jian-feng |
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| Institution: | 1. Xianning Technology College, Xianning 437100, China; 2. Department of Mathematics, Xianning College, Xianning 437100, China |
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| Abstract: | We do some research in a kind of five-order algebra curve's structure.Firstly,we change it into a counterpart Hamilton system.Then by using qualitative analysis method,considering its singular point and its character.Analysing and computing its coefficient,we find out the bifurcation of curve for its parameter plane.Then using the software of Mathematic to paint all the possible bifurcations of phase portraits.So we we finish the classifications of the algebra curve.This kind of curve can be divided into 13 types. |
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| Keywords: | Five-order algebra curve Hamilton system Bifurcation curves Phase portrait of plane Qualitative theory |
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