IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4779-d1288552.html
   My bibliography  Save this article

New Stability Results for Periodic Solutions of Generalized Van der Pol Oscillator via Second Bogolyubov’s Theorem

Author

Listed:
  • Safia Meftah

    (Laboratory of Operator Theory, EDP and Applications, Department of Mathematics, Science Exact Faculty, University of El Oued, El Oued 39000, Algeria)

  • Fares Yazid

    (Laboratory of Pure and Applied Mathematics, Amar Telidji University of Laghouat, Laghouat 03000, Algeria)

  • Tefaha Lejdel Ali

    (Laboratory of Operator Theory, EDP and Applications, Department of Mathematics, Science Exact Faculty, University of El Oued, El Oued 39000, Algeria)

  • Keltoum Bouhali

    (Department of Mathematics, College of Sciences and Arts in Ar-Rass, Qassim University, Saudi Arabia)

  • Abdelkader Moumen

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia)

  • Tariq Alraqad

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia)

  • Hicham Saber

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia)

Abstract

A certain class of nonlinear differential equations representing a generalized Van der Pol oscillator is proposed in which we study the behavior of the existing solution. After using the appropriate variables, the first Levinson’s change converts the equations into a system with two equations, and the second converts these systems into a Lipschitzian system. Our main result is obtained by applying the Second Bogolubov’s Theorem. We established some integrals, which are used to compute the average function of this system and arrive at a new general condition for the existence of an asymptotically stable unique periodic solution. One of the well-known results regarding asymptotic stability appears, owing to the Second Bogolubov’s Theorem, and the advantage of this method is that it can be applied not only in the periodic dynamical systems, but also in non-almost periodic dynamical systems.

Suggested Citation

  • Safia Meftah & Fares Yazid & Tefaha Lejdel Ali & Keltoum Bouhali & Abdelkader Moumen & Tariq Alraqad & Hicham Saber, 2023. "New Stability Results for Periodic Solutions of Generalized Van der Pol Oscillator via Second Bogolyubov’s Theorem," Mathematics, MDPI, vol. 11(23), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4779-:d:1288552
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4779/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4779/
    Download Restriction: no
    ---><---

    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:11:y:2023:i:23:p:4779-:d:1288552. 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: 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.