IDEAS home Printed from https://ideas.repec.org/p/ise/remwps/wp0702019.html
   My bibliography  Save this paper

Asymptotic Poincaré Maps along the Edges of Polytopes

Author

Listed:
  • Hassan Najafi Alishah
  • Pedro Duarte
  • Telmo Peixe

Abstract

For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model wchich encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes and edges. This piecewise linear flow is easy to compute even in higher dimensions, which allows the usage of numeric algorithms to find invariant dynamical structures such as periodic, homoclinic or heteroclinic orbits, which if robust persist as invariant dynamical structures of the original flow. We apply this method to prove the existence of chaotic behavior in some Hamiltonian replicator systems on the five dimensional simplex.

Suggested Citation

  • Hassan Najafi Alishah & Pedro Duarte & Telmo Peixe, 2019. "Asymptotic Poincaré Maps along the Edges of Polytopes," Working Papers REM 2019/70, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
  • Handle: RePEc:ise:remwps:wp0702019
    as

    Download full text from publisher

    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_070_2019.pdf
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Telmo Peixe & Alexandre A. Rodrigues, 2022. "Stability of heteroclinic cycles: a new approach," Papers 2204.00848, arXiv.org.
    2. Telmo Peixe & Alexandre A. Rodrigues, 2021. "Persistent Strange attractors in 3D Polymatrix Replicators," Papers 2103.11242, arXiv.org, revised Jan 2022.

    More about this item

    Keywords

    Flows on polytopes; Asymptotic dynamics; Heteroclinic networks; Poincaré maps; Hyperbolicity; Chaos; Evolutionary game theory;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ise:remwps:wp0702019. 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: Sandra Araújo (email available below). General contact details of provider: https://rem.rc.iseg.ulisboa.pt/ .

    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.