IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921008869.html
   My bibliography  Save this article

Fractal dimension of basin boundaries calculated using the basin entropy

Author

Listed:
  • Gusso, André
  • de Mello, Leandro E.

Abstract

The concept of basin entropy (Sb) was recently introduced as a means to characterize basins of attraction with regard to their complexity. It was also found a connection between Sb and the uncertainty exponent α. This connection allows the calculation of the fractal dimension d of the basin boundary between two basins of attraction. However, this method of calculation has not been explored in the literature. In this work we evaluate the performance of the method based upon the basin entropy in the calculation of the fractal dimension of basin boundaries. For that purpose, the method is applied to the calculation of d for several artificial uniform fractals, such as the Koch island and the Sierpinski Carpet, and the values obtained are compared with the exact dimensions obtained by analytical methods. It is concluded that excellent results are generally obtained if the boxes used in the calculation of Sb are chosen adequately, and a simple criterion for this choice is proposed. Numerical arguments are provided to justify the exclusion of small boxes with low resolution in the calculation of d. While the investigation is motivated by the calculation of d for basin boundaries, the method can be applied to any image containing two distinct regions with a boundary, whose dimension has to be determined.

Suggested Citation

  • Gusso, André & de Mello, Leandro E., 2021. "Fractal dimension of basin boundaries calculated using the basin entropy," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
  • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008869
    DOI: 10.1016/j.chaos.2021.111532
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008869
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.111532?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. Gusso, André & Viana, Ricardo L. & Mathias, Amanda C. & Caldas, Iberê L., 2019. "Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 6-16.
    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. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Daza, Alvar & Wagemakers, Alexandre & Sanjuán, Miguel A.F., 2022. "Classifying basins of attraction using the basin entropy," Chaos, Solitons & Fractals, Elsevier, vol. 159(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. Ebrahimi, Reza, 2022. "Chaos in coupled lateral-longitudinal vibration of electrostatically actuated microresonators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Luo, Shaohua & Yang, Guanci & Li, Junyang & Ouakad, Hassen M., 2022. "Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Alneamy, Ayman M., 2024. "Dynamic snap-through motion and chaotic attractor of electrostatic shallow arch micro-beams," Chaos, Solitons & Fractals, Elsevier, vol. 182(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:153:y:2021:i:p2:s0960077921008869. 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.