Bifurcations and invariant sets for a family of replicator maps from evolutionary games
Dynamical Systems
2024-12-24 v1
Abstract
We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of hyperbolic chaos for the considered map. Moreover, we also give a partial solution of an open problem formulated in \cite{Misiurewicz1}: to describe all the one-dimensional maps with all the periodic orbits having the same mean value.
Cite
@article{arxiv.2412.16379,
title = {Bifurcations and invariant sets for a family of replicator maps from evolutionary games},
author = {Sergey Kryzhevich and Yiwei Zhang and Magdalena Chmara},
journal= {arXiv preprint arXiv:2412.16379},
year = {2024}
}
Comments
19 pages, 2 figures