Persistent Strange attractors in 3D Polymatrix Replicators

TL;DR

This paper investigates a family of 3D polymatrix replicators, revealing how they exhibit bifurcations leading to chaotic dynamics and strange attractors through homoclinic cycles.

Contribution

It introduces a new class of 3D polymatrix replicators and analyzes their bifurcations and routes to chaos, including the existence of strange attractors.

Findings

Existence of suspended horseshoes in the system

Presence of persistent strange attractors within parameter intervals

Identification of the route to chaos via homoclinic cycles

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, this family exhibits suspended horseshoes and persistent strange attractors. The proof relies on the existence of a homoclinic cycle to the interior equilibrium. We also describe the phenomenological steps responsible for the transition from regular to chaotic dynamics in our system (route to chaos).