IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v172y2023ics0960077923004903.html
   My bibliography  Save this article

A multi-scale transition matrix approach to chaotic time series

Author

Listed:
  • Yuan, Qianshun
  • Zhang, Jing
  • Wang, Haiying
  • Gu, Changgui
  • Yang, Huijie

Abstract

There exist rich patterns in nonlinear dynamical processes, but they merge into averages in traditional statistics-based time series analysis. Herein the multi-scale transition matrix is adopted to display the patterns and their evolutions in several typical chaotic systems, including the Logistic Map, the Tent Map, and the Lorentz System. Compared with Markovian processes, there appear rich non-trivial patterns. The unpredictability of transitions matches almost exactly with the Lyapunov exponent. The eigenvalues decay exponentially with respect to the time scale, whose decaying exponents give us the details in the curves of Lyapunov exponent versus dynamical parameters. The evolutionary behaviors differ with each other and do not saturate to the ones for the corresponding shuffled series.

Suggested Citation

  • Yuan, Qianshun & Zhang, Jing & Wang, Haiying & Gu, Changgui & Yang, Huijie, 2023. "A multi-scale transition matrix approach to chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
  • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004903
    DOI: 10.1016/j.chaos.2023.113589
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923004903
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.113589?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. Andriana S L O Campanharo & M Irmak Sirer & R Dean Malmgren & Fernando M Ramos & Luís A Nunes Amaral, 2011. "Duality between Time Series and Networks," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    2. Yang, Yue & Yang, Huijie, 2008. "Complex network-based time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1381-1386.
    3. Yuan, Qianshun & Semba, Sherehe & Zhang, Jing & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2021. "Multi-scale transition matrix approach to time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    4. Mutua Stephen & Changgui Gu & Huijie Yang, 2015. "Visibility Graph Based Time Series Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-19, November.
    5. Wang, Xiaoyan & Han, Xiujing & Chen, Zhangyao & Bi, Qinsheng & Guan, Shuguang & Zou, Yong, 2022. "Multi-scale transition network approaches for nonlinear time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    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. Yan, Shuang & Gu, Changgui & Yang, Huijie, 2024. "Bridge successive states for a complex system with evolutionary matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    2. De Florio, Mario & Kevrekidis, Ioannis G. & Karniadakis, George Em, 2024. "AI-Lorenz: A physics-data-driven framework for Black-Box and Gray-Box identification of chaotic systems with symbolic regression," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).

    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. Yan, Shuang & Gu, Changgui & Yang, Huijie, 2024. "Bridge successive states for a complex system with evolutionary matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    2. Sudhamayee, K. & Krishna, M. Gopal & Manimaran, P., 2023. "Simplicial network analysis on EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    3. Campanharo, Andriana S.L.O. & Ramos, Fernando M., 2016. "Hurst exponent estimation of self-affine time series using quantile graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 43-48.
    4. Mondal, Mitali & Mondal, Arindam & Mondal, Joyati & Patra, Kanchan Kumar & Deb, Argha & Ghosh, Dipak, 2018. "Evidence of centrality dependent fractal behavior in high energy heavy ion interactions: Hint of two different sources," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 230-237.
    5. Carlo Mari & Cristiano Baldassari, 2023. "Optimization of mixture models on time series networks encoded by visibility graphs: an analysis of the US electricity market," Computational Management Science, Springer, vol. 20(1), pages 1-23, December.
    6. Liu, Hongzhi & Zhang, Xingchen & Zhang, Xie, 2018. "Exploring dynamic evolution and fluctuation characteristics of air traffic flow volume time series: A single waypoint case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 560-571.
    7. Yue Yang & Changgui Gu & Qin Xiao & Huijie Yang, 2017. "Evolution of scaling behaviors embedded in sentence series from A Story of the Stone," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-14, February.
    8. Chen, Yu & Ling, Guang & Song, Xiangxiang & Tu, Wenhui, 2023. "Characterizing the statistical complexity of nonlinear time series via ordinal pattern transition networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    9. Baggio, Rodolfo, 2015. "Looking into the future of complex dynamic systems," MPRA Paper 65549, University Library of Munich, Germany.
    10. Wang, Xiaoyan & Tang, Ming & Guan, Shuguang & Zou, Yong, 2023. "Quantifying time series complexity by multi-scale transition network approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    11. Yuan, Qianshun & Semba, Sherehe & Zhang, Jing & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2021. "Multi-scale transition matrix approach to time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    12. Jamshid Ardalankia & Jafar Askari & Somaye Sheykhali & Emmanuel Haven & G. Reza Jafari, 2020. "Mapping Coupled Time-series Onto Complex Network," Papers 2004.13536, arXiv.org, revised Aug 2020.
    13. Chun-Xiao Nie, 2021. "Studying the correlation structure based on market geometry," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 411-441, April.
    14. Yao, Can-Zhong & Lin, Ji-Nan & Lin, Qing-Wen & Zheng, Xu-Zhou & Liu, Xiao-Feng, 2016. "A study of causality structure and dynamics in industrial electricity consumption based on Granger network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 297-320.
    15. Xie, Wen-Jie & Zhou, Wei-Xing, 2011. "Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3592-3601.
    16. López Pérez, Mario & Mansilla Corona, Ricardo, 2022. "Ordinal synchronization and typical states in high-frequency digital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    17. Liu, Keshi & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2020. "Visibility graph analysis of Bitcoin price series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    18. Charley Presigny & Marie-Constance Corsi & Fabrizio De Vico Fallani, 2024. "Node-layer duality in networked systems," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    19. Hongduo Cao & Tiantian Lin & Ying Li & Hanyu Zhang, 2019. "Stock Price Pattern Prediction Based on Complex Network and Machine Learning," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    20. Schmidt, Jonas & Köhne, Daniel, 2023. "A simple scalable linear time algorithm for horizontal visibility graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).

    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:chsofr:v:172:y:2023:i:c:s0960077923004903. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.