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Asymptotic Poincaré Maps along the Edges of Polytopes

Author

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  • 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
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    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_070_2019.pdf
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    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.

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