基于描述函数法确定极限环个数问题的研究  

Study of Describing Function Approach on Determining Limit Cycle Number

作　　者：于威威[1] 管克英[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《北京交通大学学报》2006年第3期88-92,共5页JOURNAL OF BEIJING JIAOTONG UNIVERSITY

摘　　要：将描述函数法用于确定微分方程极限环个数的问题是一个有意义的理论探索.本文针对描述函数法适用于该问题的合理性及其局限性作了较为深入的分析,并给出了典型的例证和反例加以说明.结果证明:使用描述函数法能够简化该问题的求解,但也暴露出其存在着近似表示,频率归1以及更一般二阶系统不适用等方面的局限和不足.Using DF（Describing Function） in determining the limit cycle number of differential equation is a significant analysis try. More detailed researches are focused on discussing the rationality and restrictive ofDF problem in this paper and the typical exemplification and counterexample are presented. The results prove that DF could simplify the solve process and its shortcoming of restriction in approximately denotation, frequency unitary 1 and inapplicability in more commonly quadratic system are also shown at the same time.

关 键 词：描述函数法 极限环个数 LIENARD方程 合理性 局限性 

分 类 号：O175.14[理学—数学]