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

作　　者：刘杰 石书婷 赵军产 

机构地区：[1]Research Center of Nonlinear Science, Faculty of Mathematics and Computer Science, Wuhan Textile University [2]Department of Mathematics, Faculty of Mathematics and Computer Science, Wuhan Textile University

出　　处：《Chinese Physics B》2013年第1期131-137,共7页中国物理B（英文版）

基　　金：Project supported by the Key Project of Ministry of Education of China (Grant No. 2010141);the National Natural Science Foundation of China (Grant No. 61203159)

摘　　要：The 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.The 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 

分 类 号：O415.5[理学—理论物理]