IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v461y2016icp812-823.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116302801
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.06.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Silva, Luiz Eduardo Virgilio & Cabella, Brenno Caetano Troca & Neves, Ubiraci Pereira da Costa & Murta Junior, Luiz Otavio, 2015. "Multiscale entropy-based methods for heart rate variability complexity analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 143-152.
    2. Mukherjee, Sayan & Palit, Sanjay Kumar & Banerjee, Santo & Ariffin, M.R.K. & Rondoni, Lamberto & Bhattacharya, D.K., 2015. "Can complexity decrease in congestive heart failure?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 93-102.
    3. De Micco, Luciana & Fernández, Juana Graciela & Larrondo, Hilda A. & Plastino, Angelo & Rosso, Osvaldo A., 2012. "Sampling period, statistical complexity, and chaotic attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2564-2575.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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).
    3. 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.
    4. 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).
    5. 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.
    6. 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).
    7. 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).
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Natiq, Hayder & Banerjee, Santo & He, Shaobo & Said, M.R.M. & Kilicman, Adem, 2018. "Designing an M-dimensional nonlinear model for producing hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 506-515.
    2. Ahmed, Umair & Carpitella, Silvia & Certa, Antonella, 2021. "An integrated methodological approach for optimising complex systems subjected to predictive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Gros, Daniel & De Groen, Willem Pieter, 2015. "Will the Single Resolution Fund be a �baby tiger� during the transition?," CEPS Papers 11192, Centre for European Policy Studies.
    4. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    5. Cui, Huizi & Zhou, Lingge & Li, Yan & Kang, Bingyi, 2022. "Belief entropy-of-entropy and its application in the cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Yan, Bo & Palit, Sanjay K. & Mukherjee, Sayan & Banerjee, Santo, 2019. "Signature of complexity in time–frequency domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    7. Natiq, Hayder & Banerjee, Santo & Misra, A.P. & Said, M.R.M., 2019. "Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 58-68.
    8. Pastor, Marissa & Song, Juyong & Hoang, Danh-Tai & Jo, Junghyo, 2016. "Minimal perceptrons for memorizing complex patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 31-37.
    9. Azami, Hamed & Escudero, Javier, 2017. "Refined composite multivariate generalized multiscale fuzzy entropy: A tool for complexity analysis of multichannel signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 261-276.
    10. Mukherjee, Sayan & Banerjee, Santo & Rondoni, Lamberto, 2018. "Dispersive graded entropy on computing dynamical complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 131-140.
    11. De Micco, L. & Antonelli, M. & Larrondo, H.A., 2017. "Stochastic degradation of the fixed-point version of 2D-chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 477-484.
    12. Леиашвили, Паата, 2022. "Экономика Как Сложная Система: В Поисках Новой Парадигмы [The Economy as a Nonlinear Complex System: In Search of a New Paradigm]," MPRA Paper 114140, University Library of Munich, Germany.
    13. Chrisment, Antoine M. & Firpo, Marie-Christine, 2016. "Entropy–complexity analysis in some globally-coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 162-173.
    14. Köberle, Alexandre C. & Garaffa, Rafael & Cunha, Bruno S.L. & Rochedo, Pedro & Lucena, André F.P. & Szklo, Alexandre & Schaeffer, Roberto, 2018. "Are conventional energy megaprojects competitive? Suboptimal decisions related to cost overruns in Brazil," Energy Policy, Elsevier, vol. 122(C), pages 689-700.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:812-823. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.