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Complexity analysis of the time series using inverse dispersion entropy

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Abstract

The primary object of this study is to measure the complexity of different types of signals. We undertake the experiment to support the hypothesis of inverse dispersion entropy (IDE). Multiscale inverse dispersion entropy (MIDE) is also proposed to measure the intrinsic properties of the dynamic system. In addition, this work forms fractional inverse dispersion entropy (FIDE) and \(s^\alpha \) fractional inverse dispersion entropy (SFIDE) inspired in the properties of fractional calculus. Numerical simulations from different categories are applied to test the effectiveness of the proposed methods. Then, we apply the means to heart rate fluctuation data derived from healthy subjects and unhealthy subjects. Experimental results show that dispersion entropy and IDE can make us have a more complete understanding concerning signal complexity. Besides, MIDE method can distinguish the healthy state, pathological state and aging pattern. SFIDE is more sensitive to the change of the fractional order than FIDE.

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Acknowledgements

The financial supports from the Fundamental Research Funds for the Central Universities (2020YJS178), the funds of China Academy of Railway Science Cooperation Limited (2019YJ153) and the National Natural Science Foundation of China (61771035) are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China

    Meng Xu & Pengjian Shang

  2. P.R. China School of Environment and Natural Resources, Renmin University of China, Beijing, 100872, China

    Sheng Zhang

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  1. Meng Xu
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Xu, M., Shang, P. & Zhang, S. Complexity analysis of the time series using inverse dispersion entropy. Nonlinear Dyn 105, 499–514 (2021). https://doi.org/10.1007/s11071-021-06528-7

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