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Hopf bifurcations in delayed rock-paper-scissors replicator dynamics. (English) Zbl 1348.91051

Summary: We investigate the dynamics of three-strategy (rock-paper-scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval \(T\). Taking \(T\) as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s method.

MSC:

91A22 Evolutionary games
34K18 Bifurcation theory of functional-differential equations
37N40 Dynamical systems in optimization and economics
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