IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v171y2023ics0960077923003922.html
   My bibliography  Save this article

Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map

Author

Listed:
  • Zhao, Yifan
  • Zhang, Yongxiang

Abstract

A new route to strange nonchaotic attractors (SNAs) is investigated in a quasiperiodically driven nonsmooth map. It is shown that the smooth quasiperiodic torus becomes nonsmooth (continuous and non-differentiable) due to the border-collision bifurcation of the torus. As the coefficients change, the nonsmooth torus gets gradually fractal, forming strange nonchaotic attractors. It is termed the border-collision bifurcation route to SNAs. A novel feature of this route is that a large number of SNAs are formed, and the parameter area of SNAs makes up about 40 % of the given parameter regions. These SNAs are identified by the largest Lyapunov exponents and the phase sensitivity exponents. They are also characterized by the distribution of finite-time Lyapunov exponents. Unlike other types of SNAs, the distribution of finite-time Lyapunov exponents has its maximum at a relatively small negative Lyapunov exponent, which contributes largely to lead to the abundance of SNAs.

Suggested Citation

  • Zhao, Yifan & Zhang, Yongxiang, 2023. "Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003922
    DOI: 10.1016/j.chaos.2023.113491
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923003922
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113491?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. M., Paul Asir & K., Murali & P., Philominathan, 2019. "Strange nonchaotic attractors in oscillators sharing nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 83-93.
    2. Arulgnanam, A. & Prasad, Awadhesh & Thamilmaran, K. & Daniel, M., 2015. "Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with experimental and analytical confirmation," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 96-110.
    3. Gaolei Li & Yuan Yue & Celso Grebogi & Denghui Li & Jianhua Xie, 2021. "Strange Nonchaotic Attractors And Multistability In A Two-Degree-Of-Freedom Quasiperiodically Forced Vibro-Impact System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-13, June.
    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. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    2. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    3. Lahmiri, Salim, 2017. "Investigating existence of chaos in short and long term dynamics of Moroccan exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 655-661.
    4. Li, Gaolei & Li, Denghui & Wang, Chen & Yue, Yuan & Wen, Guilin & Grebogi, Celso, 2024. "Quantifying strange property of attractors in quasiperiodically forced systems," 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:171:y:2023:i:c:s0960077923003922. 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.