Spatial cyclic competition — spiral waves and heteroclinic orbits on the simplex
Rock (R)Paper (P)Scissors (S)
R: 0.333
P: 0.333
S: 0.333
t: 0
Three-species cyclic competition (R beats S, S beats P, P beats R) creates
heteroclinic cycles — orbits connecting saddle points on the simplex.
In the well-mixed ODE, trajectories spiral outward and approach the boundary
(extinction of two species). Spatial mixing (mobility) stabilizes spiral waves,
enabling coexistence. The simplex plot (right) tracks global frequencies.