Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

doi:10.1088/1674-1056/20/2/020505

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
Accepted manuscript online:

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(游荣义)and Huang Xiao-Jing(黄晓菁) Phase space reconstruction of chaotic dynamical system based on wavelet decomposition 2011 Chin. Phys. B 20 020505

[1]	Sun Y Z and Ruan J 2010 Chin. Phys. B 19 070513
[2]	Packard N H, Crutchfield J P, Farmer J D and Shaw R S 1980 Phys. Rev. Lett. 45 712
[3]	Takens F 1981 Lecture Notes in Mathematics 898 366
[4]	Kugiumtzis D 1996 Physica D 95 13
[5]	Kennel M B and Abarbanel H D I 2002 Phys. Rev. E 66 1
[6]	Wang A L and Yang C X 2002 Acta Phys. Sin. 51 2719 (in Chinese)
[7]	Yang S Q and Jia C Y 2002 Acta Phys. Sin. 51 2452 (in Chinese)
[8]	Wei H D, Li L P and Guo J X 2010 Chin. Phys. B 19 050505
[9]	Du L C, Dai Z C and Mei D C 2010 Chin. Phys. B 19 080503
[10]	Yang Z J and Zhao G Z 1998 Acta Biophysica Sin. 14 257 (in Chinese)
[11]	Mallat S 1989 IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI) 11 674
[12]	Shensa M J 1992 IEEE Trans. Signal Proc. 40 2464

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Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

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