Abstract
We study the replicator equations, also known as mean-field equations, for a simple model of cyclic dominance with any number $ m $ of strategies, generalizing the rock-paper-scissors model which corresponds to the case $ m = 3 $. Previously the dynamics were solved for $ m\in\{3,4\} $ by consideration of $ m-2 $ conserved quantities. Here we show that for any $ m $, the boundary of the phase space is partitioned into heteroclinic networks for which we give a precise description. A set of $ {\lfloor} m/2{\rfloor} $ conserved quantities plays an important role in the analysis. We also discuss connections to the well-mixed stochastic version of the model.
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