中国物理B ›› 2011, Vol. 20 ›› Issue (2): 20505-020505.doi: 10.1088/1674-1056/20/2/020505

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Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

游荣义, 黄晓菁   

  1. Department of Physics, School of Science, Jimei University, Xiamen 361021, China
  • 收稿日期:2010-07-05 修回日期:2010-09-05 出版日期:2011-02-15 发布日期:2011-02-15
  • 基金资助:
    Project supported by the Natural Science Foundation of Fujian Province of China (Grant Nos. 2010J01210 and T0750008).

Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

You Rong-Yi(游荣义) and Huang Xiao-Jing(黄晓菁)†   

  1. Department of Physics, School of Science, Jimei University, Xiamen 361021, China
  • Received:2010-07-05 Revised:2010-09-05 Online:2011-02-15 Published:2011-02-15
  • Supported by:
    Project supported by the Natural Science Foundation of Fujian Province of China (Grant Nos. 2010J01210 and T0750008).

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摘要： In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

关键词: chaotic dynamical system, phase space reconstruction, wavelet decomposition

Abstract: In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

Key words: chaotic dynamical system, phase space reconstruction, wavelet decomposition

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Ac (Low-dimensional chaos) 05.45.Tp (Time series analysis)