THE QUASI-FIXED-POINT TRACING METHOD FOR MULIT-PERIODIC-SOLUTIONS OF A NONLINEAR DYNAMIC SYSTEM
非线性动力系统多重周期解的伪不动点追踪法

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.