摘要
分形、分岔和混沌作为三种常见的非线性现象，它们之间是否存在什么联系？为了探索此问题，本文通过对一经典倍周期分岔模型─—Ｍａｙ模型及ＤＵｆｆｉｎｇ方程的研究，得出利用随参数变化的时间序列分维数图，可以很好地识别非线性模型从确定性状态到分岔或混沌状态的临界参数点或区域。
Being three common nonlinear phenomena: biforcation, fractal and chaos, are there relations among them? The main objective of the present work is trying to study the issue.The typical bifurcated model (May model) and Duffing equation are studied. Using the figures of fractional dimension of time series and parameter of nonlinear system, Poincare figures, phase figures and frequency spetrum figures, it is found that the critical parameters or regions of nonlinear dynnmic system from stable state to bifucation or chaotic state can be identified effectively according to the figures of fractional- dimension- trending.
出处
《工程力学》
EI
CSCD
北大核心
2000年第1期134-139,共6页
Engineering Mechanics
基金
西安交通大学研究生院博士学位论文基金
