Asymptotic Poincaré Maps along the Edges of Polytopes

Hassan Najafi Alishah, Pedro Duarte and Telmo Peixe

No 2019/70, Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa

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.

Keywords: Flows on polytopes; Asymptotic dynamics; Heteroclinic networks; Poincaré maps; Hyperbolicity; Chaos; Evolutionary game theory (search for similar items in EconPapers)
Date: 2019-02
New Economics Papers: this item is included in nep-cmp, nep-evo and nep-gth
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:ise:remwps:wp0702019

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