IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v262y1999i1p158-180.html
   My bibliography  Save this article

Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka–Volterra systems

Author

Listed:
  • Figueiredo, A.
  • Filho, T.M.Rocha
  • Brenig, L.

Abstract

We show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka–Volterra dynamical system. We show how this quasi-polynomial invariant can be decomposed in a simple manner. This decomposition permits to conclude that the existence of polynomial semi-invariants in Lotka–Volterra systems is a necessary condition for the existence of quasi-polynomial invariants. We derive a method which allows to construct the necessary conditions for existence of semi-invariants on Lotka–Volterra dynamical systems. Applications are given.

Suggested Citation

  • Figueiredo, A. & Filho, T.M.Rocha & Brenig, L., 1999. "Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka–Volterra systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 158-180.
    • Handle: RePEc:eee:phsmap:v:262:y:1999:i:1:p:158-180
    DOI: 10.1016/S0378-4371(98)00396-3
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437198003963
    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/S0378-4371(98)00396-3?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.

    References listed on IDEAS

    as
    1. Grammaticos, B. & Moulin-Ollagnier, J. & Ramani, A. & Strelcyn, J.-M. & Wojciechowski, S., 1990. "Integrals of quadratic ordinary differential equations in R3: The Lotka-Volterra system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 163(2), pages 683-722.
    2. Bountis, T.C. & Ramani, A. & Grammaticos, B. & Dorizzi, B., 1984. "On the complete and partial integrability of non-Hamiltonian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 268-288.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Figueiredo, Annibal & Rocha Filho, Tarcisio M., 2009. "Basins of attraction of invariant regular manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1877-1889.

    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. Grammaticos, B. & Moulin-Ollagnier, J. & Ramani, A. & Strelcyn, J.-M. & Wojciechowski, S., 1990. "Integrals of quadratic ordinary differential equations in R3: The Lotka-Volterra system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 163(2), pages 683-722.
    2. Antonio Jesús Pan-Collantes & Concepción Muriel & Adrián Ruiz, 2023. "Integration of Differential Equations by C ∞ -Structures," Mathematics, MDPI, vol. 11(18), pages 1-23, September.
    3. Bountis, Tassos & Tsarouhas, George, 1988. "On the application of normal forms near attracting fixed points of dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 153(1), pages 160-178.

    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:262:y:1999:i:1:p:158-180. 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: 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.