Stable and Historic Behavior in Replicator Equations Generated by Similar-Order Preserving Mappings

One could observe drastically different dynamics of zero-sum and non-zero-sum games under replicator equations. In games, heteroclinic cycles naturally occur whenever the species population supersede each other in cyclic fashion (like for Rock-Paper-Scissors game). this case, highly erratic oscillations may cause divergence time averages. contrast, it is a common belief that most “reasonable” equations satisfy “The Folk Theorem Evolutionary Game Theory” which asserts (i) Nash equilibrium rest point; (ii) stable point equilibrium; (iii) strictly asymptotically stable; (iv) any interior convergent orbit evolves to equilibrium. paper, we propose two distinct vast classes generated by similar-order preserving mappings exhibit as well mean historic behavior. latter averages will slowly oscillate during evolution system do not converge limit. This eventually higher-order repeated