A Method of Computing Kolmogorov Entropy of the Chaotic Time Series with Wavelet Packet Analysis

SHAN Hua-ning; WANG Ping-li; WANG Zhi-quan

Volume 34 Issue 1

Feb. 2005

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INFORMATION AND CONTROL > 2005 > 34(1): 12-15.

SHAN Hua-ning, WANG Ping-li, WANG Zhi-quan. A Method of Computing Kolmogorov Entropy of the Chaotic Time Series with Wavelet Packet Analysis[J]. INFORMATION AND CONTROL, 2005, 34(1): 12-15.

Citation:

SHAN Hua-ning, WANG Ping-li, WANG Zhi-quan. A Method of Computing Kolmogorov Entropy of the Chaotic Time Series with Wavelet Packet Analysis[J]. INFORMATION AND CONTROL, 2005, 34(1): 12-15.

Citation:

SHAN Hua-ning, WANG Ping-li, WANG Zhi-quan. A Method of Computing Kolmogorov Entropy of the Chaotic Time Series with Wavelet Packet Analysis[J]. INFORMATION AND CONTROL, 2005, 34(1): 12-15.

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A Method of Computing Kolmogorov Entropy of the Chaotic Time Series with Wavelet Packet Analysis

1.
Department of Automatic Control, Nanjing University of Science & Technology, Nanjing 210094, China
2.
Department of Computer Science, Nanjing University of Science & Technology, Nanjing 210094, China

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Received Date: July 20, 2004
Published Date: February 19, 2005

Graphical Abstract

Abstract

Abstract

In this paper, it is presented that Kolmogorov entropy of the chaotic signal can be computed inm-dimensional phase space with the wavelet packet transform modulus of the nonlinear time series instead of the chaotic signal itself. Based on simulation testing and noise analysis with some examples, it is found that this method is accurate and reliable. It can also overcome the noise disturbance to the signal during the sampling process.

Keywords:
chaos,
time series,
Kolmogorov entropy,
wavelet packet

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References (10)

References

[1]
Tong H.Nonlinear time series analysis since 1990:some personal reflections [J].Acta Mathematicae Applicatae Sinica(English Series), 2002,18(2):177～184.

[2]
Grassberger P, Procaccia I.Characterization of strange attractors [J].Physical Review Letters, 1983,50(5):346～349.

[3]
Finn J M, Goettee J D, Toroczkai Z, et al.Estimation of entropies and dimensions by nonlinear symbolic time series analysis [J].Chaos, 2003,13(2):444～456.

[4]
李永根,吴纪桃.分形与小波 [M].北京:科学出版社,2002.

[5]
Pommer A, Uhl A.Selective encryption of wavelet-packet encoded image data:efficiency and security [J].Multimedia Systems, 2003,9(3):279～287.

[6]
Grassberger P, Procaccia I.Estimation of the Kolmogorov entropy from a chaotic signal [J].Physical Review A, 1983,28(4):2591～2593.

[7]
Brock W A, Dechert W D, Scheinkman J A.A test for independence based on the correlation dimension [J].Econometric Reviews, 1996,15(3):197～235.

[8]
LeBaron B.A fast algorithm for the BDS statistic [J].Studies in Nonlinear Dynamics and Econometrics, 1997, 2(2):53～59.

[9]
Kim H S, Eykholt R, Salas J D.Nonlinear dynamics, delay times, and embedding windows [J].Physiea D, 1999,127(1-2):48～60.

[10]
赵贵兵,石炎福,段文锋,等.从混沌序列同时计算关联维和Kolmogorov熵[J].计算物理,1999,16(5):309～315.

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[1]	Tong H.Nonlinear time series analysis since 1990:some personal reflections [J].Acta Mathematicae Applicatae Sinica(English Series), 2002,18(2):177～184.
[2]	Grassberger P, Procaccia I.Characterization of strange attractors [J].Physical Review Letters, 1983,50(5):346～349.
[3]	Finn J M, Goettee J D, Toroczkai Z, et al.Estimation of entropies and dimensions by nonlinear symbolic time series analysis [J].Chaos, 2003,13(2):444～456.
[4]	李永根,吴纪桃.分形与小波 [M].北京:科学出版社,2002.
[5]	Pommer A, Uhl A.Selective encryption of wavelet-packet encoded image data:efficiency and security [J].Multimedia Systems, 2003,9(3):279～287.
[6]	Grassberger P, Procaccia I.Estimation of the Kolmogorov entropy from a chaotic signal [J].Physical Review A, 1983,28(4):2591～2593.
[7]	Brock W A, Dechert W D, Scheinkman J A.A test for independence based on the correlation dimension [J].Econometric Reviews, 1996,15(3):197～235.
[8]	LeBaron B.A fast algorithm for the BDS statistic [J].Studies in Nonlinear Dynamics and Econometrics, 1997, 2(2):53～59.
[9]	Kim H S, Eykholt R, Salas J D.Nonlinear dynamics, delay times, and embedding windows [J].Physiea D, 1999,127(1-2):48～60.
[10]	赵贵兵,石炎福,段文锋,等.从混沌序列同时计算关联维和Kolmogorov熵[J].计算物理,1999,16(5):309～315.

[1]	NAN Nan, ZHOU Qiang, YANG Hui, WANG Ying. The Ceramic Crack Gray Diagnosis Based on Wavelet Package Decomposition[J]. INFORMATION AND CONTROL, 2011, 40(1): 95-99,104.
[2]	YAN He, PAN Ying-jun, DONG Shi-du, LI Lei-lei, JIN Wei. A Locally Adaptive Fusion Algorithm of Remote Sensing Images in Complex Wavelet Packet Domain[J]. INFORMATION AND CONTROL, 2008, 37(4): 396-402.
[3]	YIN Guang-wei, ZHENG Pi-e. Forecasting Method of Complex System Conditions Based on Wavelet Transformation and Chaos Theory[J]. INFORMATION AND CONTROL, 2007, 36(1): 6-9.
[4]	HAN Min, LIU Yu-hua, XI Jian-hui, SHI Zhi-wei. Chaotic Signal Denoising Based on Threshold Selection of Wavelet Transform[J]. INFORMATION AND CONTROL, 2005, 34(5): 543-547.
[5]	SHI Ze-lin, LI De-qiang, HUANG Sha-bai. Fuzzy Criterion Based Wavelet Feature Selection for Face Recognition[J]. INFORMATION AND CONTROL, 2005, 34(1): 50-53,65.
[6]	CHEN Hong-wei, ZHANG Huan-chun, HUANG Guo-jian. An Image Compression Based on Wavelet Zerotree[J]. INFORMATION AND CONTROL, 2004, 33(4): 399-403.
[7]	WANG Zhen, WANG Zhi-quan, DAI Yue-wei. RESEARCH ON DIGITAL IMAGE ENCRYPTION VIA SPATIAL TRANSFORMATION[J]. INFORMATION AND CONTROL, 2002, 31(6): 518-523.
[8]	LÜ Lihua, SONG Zhi-huan, LI Ping. A NOVEL LEARNING METHOD FOR WAVELET NETWORKS[J]. INFORMATION AND CONTROL, 2002, 31(1): 14-18.
[9]	LÜ Zhao-xia, HU Wei-li. APPLICATION OF WAVELET NETWORKS ON CONTROL SYSTEM[J]. INFORMATION AND CONTROL, 2000, 29(6): 532-540.
[10]	WANG Yuping, CAI Yuanlong, GENG Zhongxing. FILTERING BASED ON WAVELET TRANSFORM[J]. INFORMATION AND CONTROL, 1996, 25(4): 199-205.

A Method of Computing Kolmogorov Entropy of the Chaotic Time Series with Wavelet Packet Analysis

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