Three-species cyclic-competition reaction-diffusion system
(Belousov–Zhabotinsky-style):
∂u/∂t − ε·Δu = α·u·(v−w) ∂v/∂t − ε·Δv = α·v·(w−u) ∂w/∂t − ε·Δw = α·w·(u−v) Conservation: ∂(u+v+w)/∂t − ε·Δ(u+v+w) = 0 — the total
of the three species is locally conserved (the reaction is
rock-paper-scissors cyclic; nothing is created or destroyed).
Random IC: spiral waves and target patterns emerge as one species
locally dominates and then is overtaken by the next in the cycle.
Vary α to control the reaction speed; the diffusion smooths the
fronts between species patches. Diffusion coef ε·dt/h² = 0.25 is
the explicit-Euler stability boundary; default 0.15 stays well
inside.
Red: u species. Blue: v species. Green: w
species. Polylines: cross-cuts of u (red), v (blue), w
(green) along j = N/2.