IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v194y2025ics0960077925002036.html
   My bibliography  Save this article

A generalized high-order correlation dimension for strange attractors

Author

Listed:
  • Weng, Tongfeng
  • Wu, Minze
  • Feng, Shiyuan
  • Chen, Xiaolu
  • Ren, Zhuoming
  • Liu, Runran
  • Small, Michael

Abstract

Correlation dimension is a well-known measurement for characterizing strange attractors but only exploring low-order correlation in complex orbit structure. We propose a generalized correlation dimension of strange attractors based on algebraic topology. By mapping a strange attractor into consecutive graphs under different similarity scales, we identify a power law relation between the number of a specific order of clique and the similarity scale, defining a finite algebraic exponent. Interestingly, we find that the algebraic exponent follows a linear growth pattern as a function of the order of clique. We demonstrate that this is a universal principle governing topological structure of strange attractors.

Suggested Citation

  • Weng, Tongfeng & Wu, Minze & Feng, Shiyuan & Chen, Xiaolu & Ren, Zhuoming & Liu, Runran & Small, Michael, 2025. "A generalized high-order correlation dimension for strange attractors," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002036
    DOI: 10.1016/j.chaos.2025.116190
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925002036
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116190?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. Vogl, Markus, 2022. "Controversy in financial chaos research and nonlinear dynamics: A short literature review," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    Full references (including those not matched with items on IDEAS)

    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. Ren, Jinfu & Liu, Yang & Liu, Jiming, 2023. "Chaotic behavior learning via information tracking," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Vogl, Markus, 2023. "Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framewo," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Wang, Qixin & Jiang, Lin & Yan, Lianshan & He, Xingchen & Feng, Jiacheng & Pan, Wei & Luo, Bin, 2024. "Chaotic time series prediction based on physics-informed neural operator," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    4. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    5. Orlando Gomes, 2024. "The emergence of chaos in productivity distribution dynamics," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(2), pages 565-596, December.
    6. Vogl, Markus & Kojić, Milena & Sharma, Abhishek & Stanisic, Nikola, 2025. "Decoding financial markets: Empirical DGPs as the key to model selection and forecasting excellence – A proof of concept," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 666(C).
    7. Vogl, Markus & Kojić, Milena & Mitić, Petar, 2024. "Dynamics of green and conventional bond markets: Evidence from the generalized chaos analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(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:194:y:2025:i:c:s0960077925002036. 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.