New predication of chaotic time series based on local Lyapunov exponent

doi:10.1088/1674-1056/22/5/050502

Abstract A new method of predicting chaotic time series is presented based on local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula using the definition of local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision than two older methods. Effects of number of referential state vectors and added noise on forecasting accuracy are also studied numerically.

Keywords: chaotic time series prediction of chaotic time series local Lyapunov exponent least squares method

Received: 11 June 2012
Revised: 17 September 2012
Accepted manuscript online:

PACS:

05.45.Ac

(Low-dimensional chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61201452).

Corresponding Authors: Zhang Yong
E-mail: ballack-13@163.com

Cite this article:

Zhang Yong (张勇) New predication of chaotic time series based on local Lyapunov exponent 2013 Chin. Phys. B 22 050502

[1]	Wolf A, Swift J B, Swinney H L and Vastan J A 1983 Phys. Rev. A 16 285
[2]	Lu S and Wang H Y 2006 Acta Phys. Sin. 54 550 (in Chinese)
[3]	Takens F 1981 Dynamical Systems and Turbulence (Berlin: Springer) p. 366
[4]	Alligood K T, Sauer T D and Yorke J A 1996 Chaos: an Introduction to Dynamical Systems (Berlin: Springer)
[5]	Abarbanel H D I, Browm R and Kennel M B 1992 J. Nonlinear Sci. 2 343
[6]	Abarbanel H D I, Browm R and Kennel M B 1991 J. Nonlinear Sci. 1 175
[7]	Christine Z, Leonard A S and Jurgen K 2000 Phys. Lett. A 271 237
[8]	Florian G and Hans H D 2005 Chao. Sol. Fract. 23 1809
[9]	Zhou Y D, Ma H and Lü W Y 2007 Acta Phys. Sin. 56 6809 (in Chinese)
[10]	Bai M, Hu K and Tang Y 2011 Chin. Phys. B 20 128902
[11]	Meng Q F, Peng Y H and Sun J 2007 Chin. Phys. 16 3220
[12]	Meng Q F, Chen Y H and P Y H 2009 Chin. Phys. B 18 2194
[13]	Zhang J S, Li H C and Xiao X C 2005 Chin. Phys. 14 49
[14]	Farmer J D and Sidorowich J J 1987 Phys. Rev. Lett. 59 845
[15]	Dominique G and Justin L 2009 Chaos Soliton. Fract. 41 2401
[16]	Li K P, Gao Z Y and Chen T L 2003 Chin. Phys. 12 1213
[17]	Zhang Y and Guan W 2009 Acta Phys. Sin. 58 756 (in Chinese)
[18]	Zhang S and Xiao X C 2005 Acta Phys. Sin. 54 5062 (in Chinese)
[19]	Ma Q L, Zhang Q L, Peng H, Zhong T W and Qin J W 2008 Chin. Phys. B 17 0536
[20]	Ding G, Zhang S S and Li Y 2008 Chin. Phys. B 17 1998
[21]	Yan H, Wei P and Xiao X C 2007 Acta Phys. Sin. 56 5111 (in Chinese)
[22]	Gan J C and Xiao X C 2007 Acta Phys. Sin. 52 2995 (in Chinese)
[23]	Meng Q F, Zhang Q and Ai W Y 2006 Acta Phys. Sin. 55 1666 (in Chinese)
[24]	Li H C, Zhang J S and Xiao X C 2005 Chin. Phys. 14 2181
[25]	Zhang J S and Xiao X C 2001 Chin. Phys. 10 390
[26]	Meng Q F, Peng Y H and Xue P J 2007 Chin. Phys. 16 1252
[27]	Grassberger P and Procaccia I 1983 Phys. Rev. Lett. 50 346
[28]	Palus M and Dvorak I 1992 Physica D 55 221
[29]	Judd K and Mees A 1998 Physica D 120 27
[30]	Kennel M, Brown R and Abarbanel H D I 1992 Phys. Rev. A 45 3403
[31]	Cao L 1997 Physica D 110 43
[32]	Sugihara G and May R M 1990 Nature 344 734
[33]	Fraser A M 1989 Physica D 34 391

[1]	A method to improve the precision of chaotic time series prediction by using a non-trajectory Yan Hua(闫华), Wei Ping(魏平), and Xiao Xian-Ci(肖先赐). Chin. Phys. B, 2009, 18(8): 3287-3294.
[2]	Regular nonlinear response of the driven Duffing oscillator to chaotic time series Yuan Ye(袁野), Li Yue(李月), Danilo P. Mandic, and Yang Bao-Jun(杨宝俊). Chin. Phys. B, 2009, 18(3): 958-968.
[3]	Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network Ma Qian-Li(马千里), Zheng Qi-Lun(郑启伦), Peng Hong(彭宏), Zhong Tan-Wei(钟谭卫), and Qin Jiang-Wei(覃姜维) . Chin. Phys. B, 2008, 17(2): 536-542.
[4]	The improved local linear prediction of chaotic time series Meng Qing-Fang(孟庆芳), Peng Yu-Hua(彭玉华), and Sun Jia(孙佳). Chin. Phys. B, 2007, 16(11): 3220-3225.
[5]	Chaotic time series prediction using fuzzy sigmoid kernel-based support vector machines Liu Han (刘涵), Liu Ding (刘丁), Deng Ling-Feng (邓凌峰). Chin. Phys. B, 2006, 15(6): 1196-1200.
[6]	Chaotic time series prediction using mean-field theory for support vector machine Cui Wan-Zhao (崔万照), Zhu Chang-Chun (朱长纯), Bao Wen-Xing (保文星), Liu Jun-Hua (刘君华). Chin. Phys. B, 2005, 14(5): 922-929.
[7]	Neural Volterra filter for chaotic time series prediction Li Heng-Chao (李恒超), Zhang Jia-Shu (张家树), Xiao Xian-Ci (肖先赐). Chin. Phys. B, 2005, 14(11): 2181-2188.
[8]	Local discrete cosine transformation domain Volterra prediction of chaotic time series Zhang Jia-Shu (张家树), Li Heng-Chao (李恒超), Xiao Xian-Ci (肖先赐). Chin. Phys. B, 2005, 14(1): 49-54.
[9]	Chaotic time series prediction using least squares support vector machines Ye Mei-Ying (叶美盈), Wang Xiao-Dong (汪晓东). Chin. Phys. B, 2004, 13(4): 454-458.
[10]	Improving the prediction of chaotic time series Li Ke-Ping (李克平), Gao Zi-You (高自友), Chen Tian-Lun (陈天仑). Chin. Phys. B, 2003, 12(11): 1213-1217.
[11]	MULTISTAGE ADAPTIVE HIGHER-ORDER NONLINEAR FINITE IMPULSE RESPONSE FILTERS FOR CHAOTIC TIME SERIES PREDICTIONS Zhang Jia-shu (张家树), Xiao Xian-ci (肖先赐). Chin. Phys. B, 2001, 10(5): 390-394.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

New predication of chaotic time series based on local Lyapunov exponent

Cite this article:

Online attention