基于小波脊线的混沌运动识别新方法

Wavelet ridge-based novel method for chaotic motion identification

基于小波脊线和混沌理论,提出了一种基于小波脊线法的混沌运动识别新方法。首先对Lorenz系统进行了从周期运动到混沌运动的详细演化分析,通过对相轨迹图、功率谱密度图和小波脊线图的对比,证明了小波脊线可以有效地区分系统的周期运动、倍周期分岔运动及混沌运动。然后通过对多个典型混沌系统进行分析,归纳总结了混沌运动在小波脊线图上表现出的规律性和细节特征。最后证明利用小波脊线法可以对混沌运动和随机噪声进行清晰的区分。

A novel method is proposed for chaos identification based on the theories of wavelet ridge line and chaos.First,the Lorenz system is applied as the research object and its evolutionary processes from periodic motion to chaotic motion are analyzed systematically.Second,the diagrams of phase trajectory,power spectral density and wavelet ridge line are compared mutually.The comparison results indicate that the motions of period,period-doubling bifurcation and chaos can be obviously distinguished using the wavelet ridge line.Finally,other three typical chaotic systems are studied,the regularity and detail features of chaotic motion reflected in the wavelet ridge line diagrams are summarized.The study results prove that the chaotic motion and the random noise can be distinguished clearly using the wavelet ridge line.