IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i9p1338-d1384771.html
   My bibliography  Save this article

On the Integrability of Persistent Quadratic Three-Dimensional Systems

Author

Listed:
  • Brigita Ferčec

    (Faculty of Energy Technology, University of Maribor, Hočevarjev trg 1, SI-8270 Krško, Slovenia
    Faculty of Natural Science and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia
    Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia)

  • Maja Žulj

    (Faculty of Energy Technology, University of Maribor, Hočevarjev trg 1, SI-8270 Krško, Slovenia)

  • Matej Mencinger

    (Faculty of Natural Science and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia
    Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia
    Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia)

Abstract

We consider a nine-parameter familiy of 3D quadratic systems, x ˙ = x + P 2 ( x , y , z ) , y ˙ = − y + Q 2 ( x , y , z ) , z ˙ = − z + R 2 ( x , y , z ) , where P 2 , Q 2 , R 2 are quadratic polynomials, in terms of integrability. We find necessary and sufficient conditions for the existence of two independent first integrals of corresponding semi-persistent, weakly persistent, and persistent systems. Unlike some of the earlier works, which primarily focus on planar systems, our research covers three-dimensional spaces, offering new insights into the complex dynamics that are not typically apparent in lower dimensions.

Suggested Citation

  • Brigita Ferčec & Maja Žulj & Matej Mencinger, 2024. "On the Integrability of Persistent Quadratic Three-Dimensional Systems," Mathematics, MDPI, vol. 12(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1338-:d:1384771
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/9/1338/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/9/1338/
    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:12:y:2024:i:9:p:1338-:d:1384771. 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.