一种确定非线性振子多个共存周期解的数值方法  

An Algorithm for Locating Coexisting Periodic Solutions of Nonlinear Oscillators

作　　者：王福新[1] 胡海岩[1] 

机构地区：[1]南京航空航天大学

出　　处：《应用力学学报》1998年第1期105-108,共4页Chinese Journal of Applied Mechanics

基　　金：航空基础科学基金;国家自然科学基金;国家教委"跨世纪优秀人才计划"基金

摘　　要：提出一种简洁高效数值方法，用以确定周期激励下非线性振子的多个共存周期响应。这是一种基于Ｐｏｉｎｃａｒé映射和二维自治系统奇点分类的几何方法，可在Ｐｏｉｎｃａｒé截面上得出多个周期运动的分布情况和类型。文中二个算例证实了该方法的有效性。A simple, but efficient numerical scheme is proposed to determine the coexisting periodic solutions of periodically forced nonlinear oscillators. This scheme is based upon the geometrical concept of the Poincare mapping and the theory of the singularity point of two dimensional autonomous systems. It can locate all periodic fixed points in a domain of concern and identify their types as well. The efficiency of the scheme is demonstrated through two examples in the paper.

关 键 词：周期解 多吸引子 Poindcare映射 胞映射 非线性振子 数值方法 

分 类 号：O322[理学—一般力学与力学基础]