IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i10p1629-d812697.html
   My bibliography  Save this article

Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint

Author

Listed:
  • Borut Zalar

    (Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, 2000 Maribor, Slovenia
    Current address: FGPA, Smetanova 17, 2000 Maribor, Slovenia.)

  • Matej Mencinger

    (Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, 2000 Maribor, Slovenia
    Institute of Mathematics Physics and Mechanics, 1000 Ljubljana, Slovenia)

Abstract

We show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra. A generalization to a three-dimensional case is considered and some counterexamples provided.

Suggested Citation

  • Borut Zalar & Matej Mencinger, 2022. "Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint," Mathematics, MDPI, vol. 10(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1629-:d:812697
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/10/1629/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/10/1629/
    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:10:y:2022:i:10:p:1629-:d:812697. 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.