Hopf Bifurcations in Two-Strategy Delayed Replicator Dynamics

We investigate the dynamics of two-strategy replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T . We analyze two models: in the first, all terms in the fitness are delayed, while in the second, only oppositestrategy terms are delayed. We compare the two models via a linear homotopy. Taking the delay T as a bifurcation parameter, we demonstrate the existence of (nondegenerate) Hopf bifurcations in both models, and present an analysis of the resulting limit cycles using Lindstedt’s method.