寻找周期轨道的代数分析法

An Algebraic Analytical Method Looking for the Periodic Orbits

本文给出了计算一般代数型（有理分式）离散动力系统周期轨道的一种分析方法—代数分析法．这种方法的优点是将非线性求解问题转化为一个线性求解问题来处理。它不仅可以准确地确定包括稳定和不稳定周期轨道的位置，而且还可以详细了解周期轨道的产生和随参数演变的分岔特性。本文利用这种方法分析了一个四维二次非线性映射，并给出了其完整的低周期轨道的分岔曲线图．

In this paper a general analytical method-an algebraic analytical me-thod-calculating the periodic orbits for an algebraic(rational fraction) discrete dy-namical system is given。It’s advantage is to transfer a nonlinear solving problem to a linear problem. It can not only exactly determine the concrete location of the sta-ble and unstable periodic orbits, but also understand the creation mechanism of these periodic orbits and their bifurcation behaviours as the parameters evolve.By us-ing this method a four dimentional quadratic nonlinear mapping is analyzied and a figure of complete bifurcation curves for the lower periodic orbits is given.