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Refined composite variable-step multiscale multimapping dispersion entropy: a nonlinear dynamical index

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Abstract

Nonlinear dynamical index can measure the complexity for a single time scale of the series, and when combined with coarse-grained methods, multiple time scales can be obtained to extract more information. In this study, a new coarse-grained method called refined composite variable-step multiscale (RCVM) is proposed, which obtains more subseries by setting different initial points and step lengths and thus extracts more potential information; moreover, in order to get a nonlinear dynamical index value with stronger stability, this study proposes the multimapping dispersion entropy (MDE) by averaging multiple classes of effective mapping approaches on the basis of dispersion entropy; by combining MDE and RCVM processing, RCVM-MDE is proposed to be used as a new nonlinear dynamical index, which can reflect the complexity of the series at multiple scales. The results of the four classes of chaotic simulated signals show that RCVM-MDE is not only able to detect the series nonlinear dynamic changes, but also has a very high stability; the results of three classes of real-world signals demonstrate the differentiability of RCVM-MDE compared to other commonly used entropies, as well as the best classification effect.

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Data availability

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

DE:

Dispersion entropy

MDE:

Multimapping dispersion entropy

RCM:

Refined composite multiscale

VM:

Variable-step multiscale

RCVM:

Refined composite variable-step multiscale

RCVM-MDE:

Refined composite variable-step multiscale multimapping dispersion entropy

M-MDE:

Multiscale multimapping dispersion entropy

M-DE:

Multiscale dispersion entropy

RCM-DE:

Refined composite multiscale dispersion entropy

M-FRDE:

Multiscale fluctuation-based reverse dispersion entropy

LM:

Linear mapping

TANSIG:

Tangent sigmoid

LOGSIG:

Logarithm sigmoid

NCDF:

Normal cumulative distribution function

SORT:

Sorting method

WGN:

White Gaussian noise

PN:

Pink noise

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61871318), Key Research and Development Projects of Shaanxi Province (No. 2022JBGS3-01), and the Natural Science Foundation of Shaanxi Province (No. 2022JM-337).

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The authors have not disclosed any funding.

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Authors and Affiliations

  1. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yuxing Li, Shangbin Jiao, Bo Geng & Yujun Li

  2. Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an University of Technology, Xi’an, 710048, China

    Yuxing Li, Shangbin Jiao & Yujun Li

  3. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Shiyi Deng

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  1. Yuxing Li
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Correspondence to Yuxing Li.

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Li, Y., Jiao, S., Deng, S. et al. Refined composite variable-step multiscale multimapping dispersion entropy: a nonlinear dynamical index. Nonlinear Dyn 112, 2119–2137 (2024). https://doi.org/10.1007/s11071-023-09145-8

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