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We have studied the methodology of estimating the embedding dimension for phase space reconstruction of chaotic time series according to the Takens theorem. We present an approach to the estimation of the embedding dimension based on the prediction of nonlinear performance. That is, we determine the embedding dimension by considering the variation of the performance of prediction model of chaotic time series with embedding dimension. Numerical simulations verify that the method is applicable for determining an appropriate embedding dimension.
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Keywords:
- chaos /
- phase space reconstruction /
- embedding dimension /
- prediction
[1] Brocker J, Engster D, Parlitz U 2009 Chaos 19 043130
[2] Wisniacki D A, Ares N, Vergini E G 2010 Phys. Rev. Lett. 25 254101
[3] Liu J H, Zhang H G, Feng J 2008 Acta Phys. Sin. 57 6868 (in Chinese)[刘金海、张化光、冯 健 2008 物理学报 57 6868]
[4] Gershenfeld N, Schoner B, Metois E 1999 Nature 397 392
[5] Hanias M P, Giannis I L, Tombras G S 2010 Chaos 20 013105
[6] Pecora L M, Moniz L, Nichols J, Carroll T L 2007 Chaos 17 013110
[7] Amritkar R E 2009 Phys. Rev. E 80 047202
[8] Cong R, Liu S L, Ma R 2008 Acta Phys. Sin. 57 7487 (in Chinese)[丛 蕊、刘树林、马 锐 2008 物理学报 57 7487]
[9] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[10] Packard N H, Crutchfield J P, Farmer, J D, Shaw R S 1980 Phy. Rev. Lett. 45 712
[11] Takens F 1981 Dynamical System and Turbulence, Lecture notes in Mathematics (Berlin: Springer) 366
[12] Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys.Sin. 59 1576 (in Chinses)[张淑清、贾 健、高 敏、韩 叙 2010 物理学报 59 1576]
[13] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese)[肖方红、阎桂荣、韩宇航 2005 物理学报 54 550]
[14] Meng Q F, Peng Y H, Xue P J 2007 Chin. Phys. 16 1252
[15] Meng Q F, Zhou W D, Chen Y H, Peng Y H 2010 Acta Phys. Sin. 59 123 (in Chinese) [孟庆芳、周卫东、陈月辉、彭玉华 2010 物理学报 59 123]
[16] Li J, Liu J H 2005 Acta Phys. Sin. 54 10 (in Chinese) [李 军、刘君华 2005 物理学报 54 10]
[17] Sugihara G, May R 1990 Nature 344 734
[18] Du D J, Li K, Fei M R 2010 Neurocomputing 73 2196
[19] Henon M 1976 Commun. Math. Phys. 50 69
[20] Broomhead D S, King G P 1986 Physica D 20 217
[21] Kennel M,Brown R, Abarbanel H D I 1992 Phys. Rev. A 45 3403
[22] Cao L 1997 Physica D 110 43
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[1] Brocker J, Engster D, Parlitz U 2009 Chaos 19 043130
[2] Wisniacki D A, Ares N, Vergini E G 2010 Phys. Rev. Lett. 25 254101
[3] Liu J H, Zhang H G, Feng J 2008 Acta Phys. Sin. 57 6868 (in Chinese)[刘金海、张化光、冯 健 2008 物理学报 57 6868]
[4] Gershenfeld N, Schoner B, Metois E 1999 Nature 397 392
[5] Hanias M P, Giannis I L, Tombras G S 2010 Chaos 20 013105
[6] Pecora L M, Moniz L, Nichols J, Carroll T L 2007 Chaos 17 013110
[7] Amritkar R E 2009 Phys. Rev. E 80 047202
[8] Cong R, Liu S L, Ma R 2008 Acta Phys. Sin. 57 7487 (in Chinese)[丛 蕊、刘树林、马 锐 2008 物理学报 57 7487]
[9] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[10] Packard N H, Crutchfield J P, Farmer, J D, Shaw R S 1980 Phy. Rev. Lett. 45 712
[11] Takens F 1981 Dynamical System and Turbulence, Lecture notes in Mathematics (Berlin: Springer) 366
[12] Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys.Sin. 59 1576 (in Chinses)[张淑清、贾 健、高 敏、韩 叙 2010 物理学报 59 1576]
[13] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese)[肖方红、阎桂荣、韩宇航 2005 物理学报 54 550]
[14] Meng Q F, Peng Y H, Xue P J 2007 Chin. Phys. 16 1252
[15] Meng Q F, Zhou W D, Chen Y H, Peng Y H 2010 Acta Phys. Sin. 59 123 (in Chinese) [孟庆芳、周卫东、陈月辉、彭玉华 2010 物理学报 59 123]
[16] Li J, Liu J H 2005 Acta Phys. Sin. 54 10 (in Chinese) [李 军、刘君华 2005 物理学报 54 10]
[17] Sugihara G, May R 1990 Nature 344 734
[18] Du D J, Li K, Fei M R 2010 Neurocomputing 73 2196
[19] Henon M 1976 Commun. Math. Phys. 50 69
[20] Broomhead D S, King G P 1986 Physica D 20 217
[21] Kennel M,Brown R, Abarbanel H D I 1992 Phys. Rev. A 45 3403
[22] Cao L 1997 Physica D 110 43
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