IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v555y2020ics0378437120302284.html
   My bibliography  Save this article

Existence and stability of periodic oscillations of a smooth and discontinuous oscillator

Author

Listed:
  • Liang, Zaitao
  • Yang, Yanjuan

Abstract

In this paper, we study the existence, multiplicity and Lyapunov stability of periodic oscillations of a SD oscillator which exhibits both discontinuous and smooth dynamics depending on the value of the smoothness parameter α. Both linear stability and nonlinear stability results are obtained. The proof is based on some stability criteria of second order differential equations combined with the quantitative information obtained by the method of upper and lower solutions. Moreover, some numerical simulations are provided to illustrate the results.

Suggested Citation

  • Liang, Zaitao & Yang, Yanjuan, 2020. "Existence and stability of periodic oscillations of a smooth and discontinuous oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120302284
    DOI: 10.1016/j.physa.2020.124511
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120302284
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.124511?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. Yang, Tao & Liu, Jiye & Cao, Qingjie, 2018. "Response analysis of the archetypal smooth and discontinuous oscillator for vibration energy harvesting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 358-373.
    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. Siewe, M. Siewe & Kenfack, W. Fokou & Kofane, T.C., 2019. "Probabilistic response of an electromagnetic transducer with nonlinear magnetic coupling under bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 26-35.
    2. Zhou, Biliu & Jin, Yanfei & Xu, Huidong, 2022. "Global dynamics for a class of tristable system with negative stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Khaje khabaz, Moahamad & Eftekhari, S. Ali & Hashemian, Mohamad & Toghraie, Davood, 2020. "Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).
    4. Han, Ning & Zhang, Hanfang & Lu, Peipei & Liu, Zixuan, 2024. "Resonance response and chaotic analysis for an irrational pendulum system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. Yang, Tao & Cao, Qingjie, 2020. "Dynamics and high-efficiency of a novel multi-stable energy harvesting system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Deng, Hang & Ye, Jimin & Huang, Dongmei, 2023. "Design and analysis of a galloping energy harvester with V-shape spring structure under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Guo, Shu-Ling & Yang, Yong-Ge & Sun, Ya-Hui, 2021. "Stochastic response of an energy harvesting system with viscoelastic element under Gaussian white noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 151(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:phsmap:v:555:y:2020:i:c:s0378437120302284. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.