| 一类含拟二次项和拟三次项的多项式系统的极限环 |
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| 引用本文： | 秦桂毅,梁德辉,黄文韬.一类含拟二次项和拟三次项的多项式系统的极限环[J].江西师范大学学报(自然科学版),2009,33(1). |
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| 作者姓名： | 秦桂毅 梁德辉 黄文韬 |
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| 作者单位： | 1. 桂林师范高等专科学校,数学与计算机科学系,广西,桂林,541001
2. 桂林电子科技大学,计算科学与数学学院,广西,桂林,541004 |
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| 基金项目： | 国家自然科学基金，广西教育厅科研项目，广西高校优秀人才培养计划 |
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| 摘 要： | 研究一类含拟二次项和拟三次项的多项式系统极限环分支问题,首先利用数学软件Mathematica计算出该系统在原点前18个奇点量的表达式,从而导出原点成为中心及最高阶细焦点的条件,并在此基础上给出了该系统在原点附近分支出5个极限环的实例.
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| 关 键 词： | 拟解析系统 奇点量 中心条件 极限环分支 |
Bifurcation of Limit Cycles for a Class of Polynomial System with Quasi Quadratic Terms and Quasi Cubic Terms |
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| QIN Gui-yi,LIANG De-hui,HUANG Wen-tao.Bifurcation of Limit Cycles for a Class of Polynomial System with Quasi Quadratic Terms and Quasi Cubic Terms[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2009,33(1). |
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| Authors: | QIN Gui-yi LIANG De-hui HUANG Wen-tao |
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| Institution: | 1.Department of Mathematics and Computer Science;Guilin Normal College;Guilin Guangxi 541001;China;2.School of Computing Science and Mathematics;Guilin University of Electronic Technology;Guilin Guangxi 541004;China |
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| Abstract: | In this paper,we study bifurcation of limit cycles for a class of polynomial system with quasi quadratic terms and quasi cubic terms. Firstly,the eighteen singular point quantities at the origin are computed by using of Mathematica.The conditions of the origin to be the center and to bethe highest degree fine focus are derived.Basing on them,this system which allows the appearance of five limit cycles in the neighborhood of origin is constructed. |
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| Keywords: | quasi analytic system singular point value center condition bifurcation of limit cycles |
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