小波变换在分叉与混沌研究中的应用<sup>*</sup>

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小波变换在分叉与混沌研究中的应用^*

基金项目: * 国家自然科学基金;国家教委博士后基金

1.
Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China;
2.
Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, P. R. China

摘要: 非线性振动系统中的运动形式有三种可能:周期运动、拟周期运动和混沌用Poincaré映射可确定出系统周期运动,用谐波小波变换可区分拟周期运动和混沌由此可准确地确定出参数空间中各种不同形式运动所对应的存在域.
- 小波变换 /
- 非线性振动 /
- 分叉 /
- 混沌
Abstract: The response of a nonlinear vibration system may be of three types, namely,periodic, quasiperiodic or chaotic. when foe parameters of foe system are changed. The periodic motions can be identified by Poincarb map, and harmonic wavelet transform(HAT) can distinguish quasiperiod from chaos, so the existing domains of differenttypes of motions of the system can be revealed in the parametric space with themethod of HWT joining with Poincare map.
- wavelet transform /
- nonlinear vibration /
- bifurcation chaos /

[1]	D.E.Newland,Wavelet analysis of vibration,Part:Theory,ASME,J.Vibration and Acoustics,116(3)(1994),409-416.
[2]	D.E.Newland,Ran dom Vibrations,Spectral and Wavelet Analysis,3rd Edition,Longman,Har-low and John Wiley,New York(1993),295-374.
[3]	C.K.Chui,An Introduction to Wavelets,Academic Press,San Diego(1992),49-74.
[4]	郑吉兵,裂纹转子的稳定性、分叉及混沌,西北工业大学博士学位论文(1996),29-41.