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Multivariate permutation entropy and its application for complexity analysis of chaotic systems

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  • He, Shaobo
  • Sun, Kehui
  • Wang, Huihai

Abstract

To measure the complexity of multivariate systems, the multivariate permutation entropy (MvPE) algorithm is proposed. It is employed to measure complexity of multivariate system in the phase space. As an application, MvPE is applied to analyze the complexity of chaotic systems, including hyperchaotic Hénon map, fractional-order simplified Lorenz system and financial chaotic system. Results show that MvPE algorithm is effective for analyzing the complexity of the multivariate systems. It also shows that fractional-order system does not become more complex with derivative order varying. Compared with PE, MvPE has better robustness for noise and sampling interval, and the results are not affected by different normalization methods.

Suggested Citation

  • He, Shaobo & Sun, Kehui & Wang, Huihai, 2016. "Multivariate permutation entropy and its application for complexity analysis of chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 812-823.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:812-823
    DOI: 10.1016/j.physa.2016.06.012
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    Cited by:

    1. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    2. Rostaghi, Mostafa & Rostaghi, Reza & Humeau-Heurtier, Anne & Azami, Hamed, 2024. "Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Zhang, Hui & Xu, Jie & Jia, Limin & Shi, Yihan, 2021. "Research on walking efficiency of passengers around corner of subway station," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    4. Wan, Li & Ling, Guang & Guan, Zhi-Hong & Fan, Qingju & Tong, Yu-Han, 2022. "Fractional multiscale phase permutation entropy for quantifying the complexity of nonlinear time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    5. Li, Binglun & Sun, Kehui & Wang, Huihai & Liu, Wenhao, 2024. "A delay-disturbance method to counteract the dynamical degradation of digital chaotic systems and its application," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    6. Peng, Yuexi & Sun, Kehui & Peng, Dong & Ai, Wei, 2019. "Dynamics of a higher dimensional fractional-order chaotic map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 96-107.
    7. Zhai, Lusheng & Wu, Yinglin & Yang, Jie & Xie, Hailin, 2020. "Characterizing initiation of gas–liquid churn flows using coupling analysis of multivariate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. He, Shaobo & Banerjee, Santo, 2018. "Multicavity formations and complexity modulation in a hyperchaotic discrete system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 366-377.
    9. Wang, Lingyu & Sun, Kehui & Peng, Yuexi & He, Shaobo, 2020. "Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    10. Zhe Chen & Yaan Li & Hongtao Liang & Jing Yu, 2019. "Improved Permutation Entropy for Measuring Complexity of Time Series under Noisy Condition," Complexity, Hindawi, vol. 2019, pages 1-12, March.

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