[1]庞金彪,侯为根.平面非线性系统中心焦点的待定系数判定法[J].南京师范大学学报(自然科学版),2011,34(03):36-43.
 Pang Jinbiao,Hou Weigen.Undetermined Coefficient Method on the Criterion of the Center-Focus for Nonlinear Planar Systems[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(03):36-43.
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平面非线性系统中心焦点的待定系数判定法()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第34卷
期数:
2011年03期
页码:
36-43
栏目:
数学
出版日期:
2011-09-20

文章信息/Info

Title:
Undetermined Coefficient Method on the Criterion of the Center-Focus for Nonlinear Planar Systems
作者:
庞金彪侯为根
安徽工业大学数理学院,安徽马鞍山243002
Author(s):
Pang JinbiaoHou Weigen
School of Mathematics and Physics,Anhui University of Technology,Maanshan 243002,China
关键词:
平面系统形式级数中心焦点
Keywords:
planar systemformal seriescenterfine focus
分类号:
O175.12
摘要:
Poincaré所创立的形式级数法和后继函数法,是判定平面非线性系统中心焦点的经典方法,这两种方法都存在计算复杂的困难.本文在形式级数法的基础上,利用待定系数法,建立关于形式级数各项系数的代数方程组,实现对平面系统中心焦点的判定和焦点量的计算;避开了后继函数法或形式级数法中所出现的两个无穷级数的乘积以及定积分计算问题,并举例说明此方法具有简洁和有效性.
Abstract:
The formal series and successive function created by Poincaré are two classical methods to determine the center focus for planar nonlinear systems but both methods have computational complexity. In this paper,following Poincaré's formal series method and the application of undetermined coefficient method,the algebraic equations of each coefficient of the formal series are formed,and the determination and focal value calculation of the center focus for planar system are confirmed. This method avoids the product of two infinite series arising from successive function or formal series method and the problem of the calculation of definite integral,and thus illustrates its simplicity and effectiveness.

参考文献/References:

[1] 张芷芬. 微分方程定性理论[M]. 北京: 科学出版社, 1985.
[2] 马知恩,周义仓. 常微分方程定性与稳定性方法[M]. 北京: 科学出版社, 2001.
[3] Luo D J,Wang X,Zhu D M,et al. Bifurcation theory and methods of dynamical systems[M]. Singapore: World Scientific Publishing,1997.
[4] Tang Yilei,Li Weigu,Zhang Zhifen. Focus-center problem of planar degenerate system[J]. J Math Anal Appl,2008 ( 345) : 934-940.
[5] 杜乃林,陈士华. 中心焦点判定的形式积分因子方法[J]. 数学杂志, 1997, 17( 2) : 232-239.
[6] 陈松林,年亚东. 一类非线性系统高阶奇点焦点量的递推计算[J]. 物理学报, 2007, 56( 4) : 1 851-1 854.
[7] 刘一戎. 一类高次奇点与无穷远点的中心焦点理论[J]. 中国科学: A 辑, 2001, 31( 1) : 37-48.
[8] Wu Chengqiang. The criterion of the center-focus for a class of planar perturbed polynomial systems[J]. J Math Anal Appl, 2006( 319) : 732-739.
[9] 罗定军,张祥,董梅芳. 动力系统的定性与分支理论[M]. 北京: 科学出版社, 2001.

备注/Memo

备注/Memo:
通讯联系人:庞金彪,副教授,研究方向: 微分方程定性理论. E-mail: pjbll@ ahut. edu. Cn
更新日期/Last Update: 2011-09-15