Turing in Ecology
When prey diffuses faster than predator, the homogeneous coexistence equilibrium becomes unstable — creating spatial patterns (spots, stripes) even though neither species alone would form them. This is Turing's diffusion-driven instability.
∂u/∂t = f(u,v) + Dᵤ∇²u
∂v/∂t = g(u,v) + D_v∇²v
Turing: D_v/Dᵤ >> 1
∂v/∂t = g(u,v) + D_v∇²v
Turing: D_v/Dᵤ >> 1
Parameters
Prey (green)
Predator (red)
0
Step
—
Pattern
0.0
Mean prey
0.0
Mean pred