Abstract
We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, each element of the family can be C2-approximated by a vector field whose flow exhibits suspended horseshoes and persistent strange attractors. The proof relies on the numerically observed Shilnikov homoclinic cycle to the interior equilibrium. We also describe the phenomenological steps responsible for the transition from regular to chaotic dynamics in the family (route to chaos).
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