IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-009-2975-3_26.html

Lotka-Volterra Models: Partial Stability and Partial Ultimate Bounded-Ness

In: Biomathematics and Related Computational Problems

Author

Listed:
  • P. Fergola

    (Università di Napoli, Dipartimento di Matematica e Applicazioni “R.Caccioppoli”)

  • C. Tenneriello

    (Università di Napoli, Dipartimento di Matematica e Applicazioni “R.Caccioppoli”)

Abstract

Stability and boundedness properties for autonomous and non-autonomous Lotka-Volterra systems with respect to a part only of the state variables have been studied. In the autonomous case sufficient conditions for partial asymptotic stability in the large of partially feasible equilibria have been obtained. In the nonautonomous case, due to the general non equilibrium features, it is interesting to investigate attractivity properties of suitable compact sets in the species space. Such an analysis has been performed for some classes of nonautonomous Lotka-Volterra systems for which we proved results concerning with the partial ultimate boundedness. Some of these results can be viewed as persistence criteria for a part only of the actually present species. The used approach is based on the construction of Lyapunov-like functions whose structure together with the amplitude of the time fluctuations of the parameters influence the shape and the size of the attractivity compact regions.

Suggested Citation

  • P. Fergola & C. Tenneriello, 1988. "Lotka-Volterra Models: Partial Stability and Partial Ultimate Bounded-Ness," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 283-294, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_26
    DOI: 10.1007/978-94-009-2975-3_26
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-94-009-2975-3_26. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.