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基于径向基神经网络预测的混沌时间序列嵌入维数估计方法

李鹤 杨周 张义民 闻邦椿

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基于径向基神经网络预测的混沌时间序列嵌入维数估计方法

李鹤, 杨周, 张义民, 闻邦椿

Methodology of estimating the embedding dimension in chaos time series based on the prediction performance of radial basis function neural networks

Li He, Yang Zhou, Zhang Yi-Min, Wen Bang-Chun
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  • 根据Takens定理,研究了混沌时间序列相空间重构嵌入维数的选取问题.提出了基于径向基函数神经网络预测模型性能的嵌入维数估计方法,即根据嵌入维数与混沌时间序列预测模型性能的变化关系来确定嵌入维数.通过对几种典型混沌动力学系统的数值验证,结果表明该方法能够确定出合适的相空间重构嵌入维数.
    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.
    • 基金项目: 教育部新世纪优秀人才支持计划(批准号:NCET-10-0271),机械系统与振动国家重点实验室开放课题(批准号:MSV-2011-19)教育部长江学者与创新团队发展计划(批准号:IRT0816),国家自然科学基金(批准号:10702014),中央高校基本科研业务费专项资金(批准号:N100503002,N100703001)资助的课题.
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    Hanias M P, Giannis I L, Tombras G S 2010 Chaos 20 013105

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    Pecora L M, Moniz L, Nichols J, Carroll T L 2007 Chaos 17 013110

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    Amritkar R E 2009 Phys. Rev. E 80 047202

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    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]

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    Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536

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    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]

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    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]

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    Meng Q F, Peng Y H, Xue P J 2007 Chin. Phys. 16 1252

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    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

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    Kennel M,Brown R, Abarbanel H D I 1992 Phys. Rev. A 45 3403

    [22]

    Cao L 1997 Physica D 110 43

  • [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

计量
  • 文章访问数:  9003
  • PDF下载量:  950
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-07-09
  • 修回日期:  2010-09-15
  • 刊出日期:  2011-07-15

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