IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v194y2025ics0960077925002358.html
   My bibliography  Save this article

Influence of high order nonlinearity on chaotic bursting structure in slow–fast dynamics

Author

Listed:
  • Chen, Yeqiang
  • Zhang, Miaorong
  • Zhang, Xiaofang
  • Bi, Qinsheng

Abstract

Nonlinear truncation based on Taylor expansion has widely been used for the analysis of a real model, while the order of truncation may lead to different behaviors. This paper devotes to investigate the influence of the cubic and fifth order nonlinearity on the bursting oscillations in a relatively simple slow–fast chaotic model. To reveal the characteristics of spiking oscillations, we propose a new type of cross-section based on the excitation, which can be used to compute the projections of Poincaré map conveniently. Higher order nonlinear term may result in more fine structures in a chaotic bursting attractor, implying the trajectory for spiking state alternates between more types of regular oscillations and chaos in turn. Since there exist two choices when the trajectory moving along an equilibrium branches to a pitchfork bifurcation point, it needs two neighboring periods of excitation for the trajectory to finish one cycle of the quiescent and spiking state.

Suggested Citation

  • Chen, Yeqiang & Zhang, Miaorong & Zhang, Xiaofang & Bi, Qinsheng, 2025. "Influence of high order nonlinearity on chaotic bursting structure in slow–fast dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002358
    DOI: 10.1016/j.chaos.2025.116222
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925002358
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116222?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.

    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:s0960077925002358. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.