Reaction-diffusion PDE with cross-diffusion · Turing pattern formation
Turing instability: a stable homogeneous steady state becomes unstable to spatial perturbations when predators diffuse much faster than prey (D_v ≫ D_u). This generates stationary patterns — spots, stripes, labyrinths — without external forcing. Key condition: the activator (prey) must self-activate and diffuse slowly; the inhibitor (predator) must diffuse rapidly.