New predication of chaotic time series based on local Lyapunov exponent

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

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 50502-050502.doi: 10.1088/1674-1056/22/5/050502

New predication of chaotic time series based on local Lyapunov exponent

张勇

Department of Mathematics and Computer, Wuhan Polytechnic University, Wuhan 430024, China

收稿日期:2012-06-11 修回日期:2012-09-17 出版日期:2013-04-01 发布日期:2013-04-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61201452).

New predication of chaotic time series based on local Lyapunov exponent

Zhang Yong (张勇)

Department of Mathematics and Computer, Wuhan Polytechnic University, Wuhan 430024, China

Received:2012-06-11 Revised:2012-09-17 Online:2013-04-01 Published:2013-04-01
Contact: Zhang Yong E-mail:ballack-13@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61201452).

摘要/Abstract

摘要： 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.

关键词: chaotic time series, prediction of chaotic time series, local Lyapunov exponent, least squares method

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.

Key words: chaotic time series, prediction of chaotic time series, local Lyapunov exponent, least squares method

中图分类号: (Low-dimensional chaos)

05.45.Ac

张勇. New predication of chaotic time series based on local Lyapunov exponent[J]. 中国物理B, 2013, 22(5): 50502-050502.

Zhang Yong (张勇). New predication of chaotic time series based on local Lyapunov exponent[J]. Chin. Phys. B, 2013, 22(5): 50502-050502.

参考文献 33

[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

New predication of chaotic time series based on local Lyapunov exponent

New predication of chaotic time series based on local Lyapunov exponent

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