IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i21p3368-d1507842.html
   My bibliography  Save this article

Dynamics of Some Perturbed Morse-Type Oscillators: Simulations and Applications

Author

Listed:
  • Nikolay Kyurkchiev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria
    Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria)

  • Tsvetelin Zaevski

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria)

  • Anton Iliev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria)

  • Todor Branzov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria)

  • Vesselin Kyurkchiev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria)

  • Asen Rahnev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria)

Abstract

The purpose of this paper is to investigate some Morse-type oscillators. In its original form, it is a model for describing the vibrations of a diatomic molecule. The Morse potential generalizes the harmonic oscillator by introducing deviations from the classical theoretical model. In the present study, we perturbed the Morse differential equation by several periodic terms based on the cosine function and by a damping term. The frequency is driven by different coefficients. The size of the deviations is controlled by another constant. We provide two modifications w.r.t. the damping term. The Melnikov approach is applied as an indicator of the possible chaotic opportunities. We also propose a novel approach for stochastic control of the perturbations. It is based on the assumption that the coefficients of the periodic terms are the probabilities of underlying distribution. As a result, the dynamics are driven by its characteristic function. Several applications are considered. We demonstrate some specialized modules for investigating the dynamics of the proposed models, along with the synthesis of radiating antenna patterns.

Suggested Citation

  • Nikolay Kyurkchiev & Tsvetelin Zaevski & Anton Iliev & Todor Branzov & Vesselin Kyurkchiev & Asen Rahnev, 2024. "Dynamics of Some Perturbed Morse-Type Oscillators: Simulations and Applications," Mathematics, MDPI, vol. 12(21), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3368-:d:1507842
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/21/3368/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/21/3368/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nikolay Kyurkchiev, 2020. "Some Intrinsic Properties of Tadmor–Tanner Functions: Related Problems and Possible Applications," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    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. Maria T. Vasileva, 2023. "On Topp-Leone-G Power Series: Saturation in the Hausdorff Sense and Applications," Mathematics, MDPI, vol. 11(22), pages 1-11, November.

    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:12:y:2024:i:21:p:3368-:d:1507842. 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.