Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

doi:10.1088/1674-1056/22/1/010505

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 10505-010505.doi: 10.1088/1674-1056/22/1/010505

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

刘杰^a, 石书婷^b, 赵军产^b

a Research Center of Nonlinear Science, Faculty of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China;
b Department of Mathematics, Faculty of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China

收稿日期:2012-08-23 修回日期:2012-09-24 出版日期:2012-12-01 发布日期:2012-12-01
基金资助:
Project supported by the Key Project of Ministry of Education of China (Grant No. 2010141) and the National Natural Science Foundation of China (Grant No. 61203159).

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

Liu Jie (刘杰)^a, Shi Shu-Ting (石书婷)^b, Zhao Jun-Chan (赵军产)^b

a Research Center of Nonlinear Science, Faculty of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China;
b Department of Mathematics, Faculty of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China

Received:2012-08-23 Revised:2012-09-24 Online:2012-12-01 Published:2012-12-01
Contact: Liu Jie E-mail:liujie_hch@163.com
Supported by:
Project supported by the Key Project of Ministry of Education of China (Grant No. 2010141) and the National Natural Science Foundation of China (Grant No. 61203159).

摘要/Abstract

摘要： Three most widely used methods for reconstructing the underlying time series via the recurrence plots (RPs) of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.

关键词: recurrence plot, chaotic system, time series analysis, correlation analysis

Abstract: Three most widely used methods for reconstructing the underlying time series via the recurrence plots (RPs) of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.

Key words: recurrence plot, chaotic system, time series analysis, correlation analysis

中图分类号: (Time series analysis)

05.45.Tp

05.45.Ac (Low-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)

刘杰, 石书婷, 赵军产. Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems[J]. Chin. Phys. B, 2013, 22(1): 10505-010505.

Liu Jie (刘杰), Shi Shu-Ting (石书婷), Zhao Jun-Chan (赵军产). Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems[J]. Chin. Phys. B, 2013, 22(1): 10505-010505.

参考文献 20

[1]	Ekmann J P, Kamphorst S O and Ruelle D 1987 Europhys. Lett. 4 973
[2]	Marwan N, Romano M C, Thiel M and Kurths J 2007 Phys. Rep. 438 237
[3]	Trulla L L, Giuliani A, Zbilut J P and Webber C L, 1996 Phys. Lett. A 223 255
[4]	Zbilut J P and Webber C L 1998 Phys. Lett. A 246 122
[5]	Zbilut J P, Giuliani A and Webber C L 2000 Phys. Lett. A 267 174
[6]	Thiel M, Romano M and Kurths J 2004 Phys. Lett. A 330 343
[7]	Thiel M, Romano M, Kurths J, Rolfs M and Kliegl R 2008 Phil. Trans. R. Soc. A 366 545
[8]	Hirata Y, Horai S and Aihara K 2008 Eur. Phys. J. 164 13
[9]	Gutierrez E and Zaldivar J M 2000 Earthquake Eng. Struct. Dyn. 29 1261
[10]	Atay F M and Altintas Y 1999 Phys. Rev. E 59 6593
[11]	Strozzi F, Zaldivar J M, Pioljansek K, Bono F and Gutierrez E 2009 EUR-Scientific and Technical Research Series (Luxembourg) pp. 1-56
[12]	Tenenbaum J B, de Silva V and Langford J C 2000 Science 290 2319
[13]	Lorenz E N 1963 J. Atmos. Sci. 20
[14]	Kantz H and Schreiber T 2003 Nonlinear Time Series Analysis (Cambridge: Cambridge University Press)
[15]	Donner R V, Small M, Donges J F, Marwan N, Zou Y, Xiang R and Kurths J 2011 Int. J. Bifurcat. Chaos. 21 1019
[16]	Bian H R, Wang J, Han C X, Deng B, Wei X L and Che Yan Q 2011 Acta Phys. Sin. 60 118701 (in Chinese)
[17]	Xie Y, Xu J X, Kang Y M, Yang H J and Hu S J 2003 Acta Phys. Sin. 52 1121 (in Chinese)
[18]	Xia H C and Zhan Y Q 2004 Acta Phys. Sin. 53 1299 (in Chinese)
[19]	Chen S G and Yang Z A 1997 Chin. Phys. 6 172
[20]	Xia H C and Zhan Y Q 2004 Chin. Phys. 13 1299

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

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