IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p673-d755299.html
   My bibliography  Save this article

Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System

Author

Listed:
  • Chun Zhang

    (School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China)

  • Qiaoxia Tang

    (School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China)

Abstract

The main task of this article is to study the patterns of mixed-mode oscillations and non-smooth behaviors in a Filippov system with external excitation. Different types of periodic spiral crossing mixed-mode oscillation patterns, i.e., “cusp-F − /fold-F − ” oscillation, “cusp-F − /two-fold/two-fold/fold-F − ” oscillation and “two-fold/fold-F − ” oscillation, are explored. Based on the analysis of the equilibrium and tangential singularities of the fast subsystem, spiral crossing oscillation around the tangential singularities is investigated. Meanwhile, by combining the fast and slow analysis methods, we can observe that the cusp, two-fold and fold-cusp singularities play an important role in generating all kinds of complex mixed-mode oscillations.

Suggested Citation

  • Chun Zhang & Qiaoxia Tang, 2022. "Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:673-:d:755299
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/673/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/673/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ma, Xindong & Yu, Yue & Wang, Lifeng, 2021. "Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Santolo Meo & Luisa Toscano, 2021. "On the Existence and Uniqueness of the ODE Solution and Its Approximation Using the Means Averaging Approach for the Class of Power Electronic Converters," Mathematics, MDPI, vol. 9(10), pages 1-12, May.
    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. Song, Jian & Liu, Shenquan & Wen, Qixiang, 2022. "Geometric analysis of the spontaneous electrical activity in anterior pituitary corticotrophs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Danjin Zhang & Youhua Qian, 2023. "Bursting Oscillations in General Coupled Systems: A Review," Mathematics, MDPI, vol. 11(7), pages 1-16, April.
    3. Surendar, R. & Muthtamilselvan, M. & Ahn, Kyubok, 2024. "Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 181(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:gam:jmathe:v:10:y:2022:i:5:p:673-:d:755299. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.