Heteroclinic Cycle — Symmetry Network Dynamics

A heteroclinic cycle connects saddle equilibria via their unstable manifolds. In the May-Leonard system, species 1 beats 2, 2 beats 3, 3 beats 1 (rock-paper-scissors). The simplex corner fixed points are connected by heteroclinic orbits; trajectories spiral outward toward the boundary, spending ever-longer near each vertex — a hallmark of Milnor attractors. Noise ε perturbs away from the boundary, creating stochastic switching.