非线性动力系统多重周期解的伪不动点追踪法

提出一种求解非线性动力系统多重周期解的新的思路和方法（伪不动点追踪法）；这一方法由寻找非线性动力系统同时存在的各个周期解间的联系入手；引入一个反映系统全局瞬态信息的标量函数，将非线性动力系统求各个周期解的问题转化为此标量函数的寻优问题．文中以布鲁塞尔振子及轴承转子系统为例。顺序求得了Ｔ，３Ｔ，４Ｔ，…周期解，从而得到了一些新的现象和结论

THE QUASI-FIXED-POINT TRACING METHOD FOR MULIT-PERIODIC-SOLUTIONS OF A NONLINEAR DYNAMIC SYSTEM

The Multi-Periodic-Solutions of a nonlinear dynamic system means that there existseveral periodic solutions in state space at the same time, it is determined by the nature of thenonlinear dynamic system and is an important characteristics of the nonlinear dynamic systemdiffering from the linear systems. Today the research of linear system is mature, but that of nonlinear system is very difficult. The problem of Multi-Periodic-Solutions of the nonlinear dynamicsystem is a very important and very complex problem in nonlinear research. This paper presentsa new idea and method (Quajsi-Fixed-Point Tracing Method) to get the Multi-Periodic-Solutionsof a nonlinear dynamic system. In order to find out the relation among periodic solutions of thenonlinear dynamic system, this method introduces a scalax function which includes the globaltransient information, then the problem of periodic solutions is translated into a global (or local)optimization problem of this function. Using the Brussellator oscillator and a bearing-rotor systemajs examples, we get the T, 2T, 4T,' periodic solutions of these system. Some new phenomenonand results airs given in this paper. This paper offers some references for the problem of periodicsolutions structure of the nonlinear dynamic system.