«Previous Article|Table of Contents|Next Article»

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:

2011年03期

Page:

36-43

Research Field:

数学

Publishing date:

Info

Title:

Undetermined Coefficient Method on the Criterion of the Center-Focus for Nonlinear Planar Systems

Author(s):

Pang Jinbiao; Hou Weigen

School of Mathematics and Physics,Anhui University of Technology,Maanshan 243002,China

Keywords:

planar system; formal series; center; fine focus

PACS:

O175.12

DOI:

-

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．

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．

Memo

Memo:

-

Common functions

Last Update: 2011-09-15