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Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction

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Frontiers of Electrical and Electronic Engineering in China

Abstract

A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction. It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay, which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement (AD) in AD algorithm. Thereafter, by means of the iterative algorithm of multiple autocorrelation and Γ test, the near-optimum parameters of embedding dimension and delay time are estimated. This algorithm is provided with a sound theoretic basis, and its computing complexity is relatively lower and not strongly dependent on the data length. The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4% when using conventional algorithm to 1.06% when using this algorithm. The accuracy of invariants in phase space reconstruction is greatly improved.

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Authors and Affiliations

  1. Research Institute of High Technology, Xi’an, 710025, China

    Ma Hong-guang & Han Chong-zhao

Authors
  1. Ma Hong-guang
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  2. Han Chong-zhao
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Corresponding author

Correspondence to Ma Hong-guang.

Additional information

Translated from Journal of Xi’an Jiaotong University, 2004, 38(4): 335–338 (in Chinese)

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Ma, Hg., Han, Cz. Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction. Front. Electr. Electron. Eng. China 1, 111–114 (2006). https://doi.org/10.1007/s11460-005-0023-7

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  • DOI: https://doi.org/10.1007/s11460-005-0023-7

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