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Chin. Phys. B, 2011, Vol. 20(2): 020505    DOI: 10.1088/1674-1056/20/2/020505
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Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

You Rong-Yi, Huang Xiao-Jing
Department of Physics, School of Science, Jimei University, Xiamen 361021, China
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.
Keywords:  chaotic dynamical system      phase space reconstruction      wavelet decomposition  
Received:  05 July 2010      Revised:  05 September 2010      Published:  15 February 2011
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Ac (Low-dimensional chaos)  
  05.45.Tp (Time series analysis)  
  05.45.Ca  
Fund: Project supported by the Natural Science Foundation of Fujian Province of China (Grant Nos. 2010J01210 and T0750008).

Cite this article: 

You Rong-Yi, Huang Xiao-Jing Phase space reconstruction of chaotic dynamical system based on wavelet decomposition 2011 Chin. Phys. B 20 020505

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