| 一类五次微分系统的定性分析 |
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| 引用本文： | 卢景苹,黄文韬.一类五次微分系统的定性分析[J].数学的实践与认识,2013,43(4):225-231. |
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| 作者姓名： | 卢景苹 黄文韬 |
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| 作者单位： | 1. 广西民族师范学院 数学与计算机科学系,广西崇左,532200
2. 桂林电子科技大学数学与计算科学学院,广西桂林,541004 |
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| 基金项目： | 国家自然科学基金(10961011);广西教育厅高校科研项目(201204LX482) |
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| 摘 要： | 对一类五次平面多项式微分系统进行了定性分析.给出原点的中心与等时中心条件及极限环的存在性.研究了此系统无穷远点的性态,该无穷远点是高次奇点,并运用把大角域分为若干小角域的方法对此高次奇点在不定号情形下轨线的分布情况进行讨论.
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| 关 键 词： | 极限环 无穷远点 中心 等时中心 高次奇点 |
On Qualitative Analysis for a Class of Fifth Differential Systems |
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| LU Jing-ping
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HUANG Wen-tao.On Qualitative Analysis for a Class of Fifth Differential Systems[J].Mathematics in Practice and Theory,2013,43(4):225-231. |
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| Authors: | LU Jing-ping HUANG Wen-tao |
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| Institution: | 1.Department of Mathematics and Computer Science,Guangxi Normal University for Nationalities,Chongzuo 532200,China) (2.School of Computing Science and Mathematics,Guilin University of Electronic Technology,Guilin 541004, China) |
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| Abstract: | In this paper,the qualitative nature for a class of fifth planar polynomial differential system is investigated.The conditions of center and isochronous center and the existence of limit cycles are given.At the same time,the properties of system at infinity which is a higher order singular point is investigated,and the distribution of trajectories of higher order singular point in the case of undetermined signs is discussed by the method of dividing bighorn domain into several small-angle domain. |
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| Keywords: | limit cycle infinity center isochronous center higher order singular point |
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