Spatial Predator-Prey — Turing Instability

Reaction-diffusion Lotka-Volterra: diffusion-driven instability creates spatial patterns

Step: 0 ⟨u⟩ prey: — ⟨v⟩ pred: — D_v/D_u: —
About: Spatial Lotka-Volterra with diffusion: du/dt = ru(1-u/K) - auv + D_u∇²u and dv/dt = -dv + buv + D_v∇²v. When D_v/D_u is large enough, a Turing instability occurs: a homogeneous steady state becomes unstable to spatial perturbations, generating spontaneous patterns — spots, stripes, or labyrinthine structures — even from random initial noise.