平面非线性系统中心焦点的待定系数判定法  

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

作　　者：庞金彪[1] 侯为根[1] 

机构地区：[1]安徽工业大学数理学院,安徽马鞍山243002

出　　处：《南京师大学报（自然科学版）》2011年第3期36-43,共8页Journal of Nanjing Normal University(Natural Science Edition)

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.The formal series and successive function created by Poincare are two classical methods to determine the center focus for planar nonlinear systems but both methods have computational complexity. In this paper, following Poincare＇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.

关 键 词：平面系统 形式级数 中心 焦点 

分 类 号：O151.2[理学—数学]