May-Leonard Heteroclinic CycleRock-Paper-Scissors · Non-transitive Competition

Parameters

Species 1
Species 2
Species 3
Current Phase
May-Leonard (1975):
ẋᵢ = xᵢ(1 − xᵢ − αxⱼ − βxₖ)

RPS ordering: 1 beats 2, 2 beats 3, 3 beats 1. With α≠β, heteroclinic cycles appear — orbits spiral toward corners, then switch dominance. This is not a limit cycle — it's a heteroclinic network with algebraically slow transitions. Real ecosystems show this in cyclic food webs.