Simplex phase portrait (x+y+z=1)
Parameters
Rock
Paper
Scissors
State
Rock x—
Paper y—
Scissors z—
t0
Physics
With σ=1, δ=0: trajectories spiral outward along the heteroclinic cycle — a triangle of saddle connections. Each corner is an unstable equilibrium.
Adding δ>0 stabilizes the interior coexistence point. Mutation breaks the cycle, creating limit cycles.
Adding δ>0 stabilizes the interior coexistence point. Mutation breaks the cycle, creating limit cycles.