IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v569y2021ics0378437121000595.html
   My bibliography  Save this article

On the stability of equilibrium states of the dynamical systems in critical cases

Author

Listed:
  • Barsuk, Alexandr A.
  • Paladi, Florentin

Abstract

The stability of equilibrium states described by an autonomous system of linear differential equations with constant real coefficients is studied. The cases when, among the eigenvalues of the matrix of coefficients of the system, there are simple or multiple zero eigenvalues or complex eigenvalues with zero real part (critical cases of the Lyapunov’s general theory of stability) are discussed in detail. Stability criteria for the equilibrium states in critical cases are formulated using only information about the order of the matrix of coefficients, rank of the corresponding λ-matrix, and the multiplicity of the corresponding eigenvalues without reducing to the Jordan canonical form. Particular examples of the use of the proposed stability criteria are given. The dynamics of phase transitions due to thermal fluctuations for systems described by the Landau-type kinetic potential is discussed separately. An identity is given for matrices with a zero determinant and a given rank, which can be used to analyze the stability of solutions of linear dynamical systems.

Suggested Citation

  • Barsuk, Alexandr A. & Paladi, Florentin, 2021. "On the stability of equilibrium states of the dynamical systems in critical cases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    • Handle: RePEc:eee:phsmap:v:569:y:2021:i:c:s0378437121000595
    DOI: 10.1016/j.physa.2021.125787
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121000595
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.125787?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:phsmap:v:569:y:2021:i:c:s0378437121000595. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.