Asymptotic dynamics of Hamiltonian polymatrix replicators

Abstract

Abstract In a previous paper (Alishah et al 2019 Nonlinearity 33 469) we have studied flows defined on polytopes, presenting a method to encapsulate its asymptotic dynamics along the edge-vertex heteroclinic network. Using this result we study here the Hamiltonian character of the asymptotic dynamics of conservative polymatrix replicators. Our main result states that for such conservative polymatrix replicator systems the map describing its asymptotic dynamics is Hamiltonian with respect to some appropriate Poisson structure.