Lotka-Volterra reaction-diffusion — spiral waves and Turing-like patterns
Prey: — | Predator: —
Reaction-diffusion Lotka-Volterra on a 100×100 grid:
∂u/∂t = Du·∇²u + r·u(1−u) − a·u·v (prey: green)
∂v/∂t = Dv·∇²v + b·a·u·v − d·v (predator: red)
Diffusion ratio Du/Dv drives Turing-like spiral wave instabilities.
When Du > Dv, spatial patterns emerge — predator chases prey in rotating spirals,
enabling coexistence that would collapse in a well-mixed system.
Left half: prey density (green). Right half: predator density (red).