IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i8p1260-d1380122.html
   My bibliography  Save this article

On a Family of Hamilton–Poisson Jerk Systems

Author

Listed:
  • Cristian Lăzureanu

    (Department of Mathematics, Politehnica University Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania
    Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timşoara, Parvan Blv. 4, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Jinyoung Cho

    (Department of Mathematics, Politehnica University Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania
    Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timşoara, Parvan Blv. 4, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

Abstract

In this paper, we construct a family of Hamilton–Poisson jerk systems. We show that such a system has infinitely many Hamilton–Poisson realizations. In addition, we discuss the stability and we prove the existence of periodic orbits around nonlinearly stable equilibrium points. Particularly, we deduce conditions for the existence of homoclinic and heteroclinic orbits. We apply the obtained results to a family of anharmonic oscillators.

Suggested Citation

  • Cristian Lăzureanu & Jinyoung Cho, 2024. "On a Family of Hamilton–Poisson Jerk Systems," Mathematics, MDPI, vol. 12(8), pages 1-12, April.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1260-:d:1380122
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/8/1260/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/8/1260/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cristian Lăzureanu & Jinyoung Cho, 2023. "On Hopf and Fold Bifurcations of Jerk Systems," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    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. Cristian Lăzureanu, 2023. "On the Double-Zero Bifurcation of Jerk Systems," Mathematics, MDPI, vol. 11(21), pages 1-12, October.

    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:8:p:1260-:d:1380122. 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.