  For a class of flows on polytopes, including many examples from Evolutionary
Game Theory, we describe a piecewise linear model which 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.
