Predator-Prey — Spatial Invasion Waves

Reaction-diffusion Lotka-Volterra: traveling waves and spiral patterns

Spatial Lotka-Volterra

Adding diffusion to the predator-prey model produces traveling invasion waves and Turing-like spirals:

∂u/∂t = D_u∇²u + αu − βuv
∂v/∂t = D_v∇²v + δuv − γv

u = prey (green), v = predators (red). Waves propagate as predators invade prey-rich areas, then collapse, then recover.

Key phenomena: wave pinning, spiral waves, spatiotemporal chaos for strong coupling.

Prey (u)
Predator (v)