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

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.