Klausmeier model — water-biomass Turing instability
Mean biomass: — | Pattern: —
Klausmeier (1999): ∂B/∂t = WB² − νB + D_B∇²B, ∂W/∂t = A − W − WB² + D_W∇²W.
Plants (B) concentrate water (W) via positive feedback — runoff redistribution creates spatial patterns.
High A: uniform vegetation. Decreasing A: spots → labyrinths → gaps → bare ground (desertification).
This is a Turing-type instability: diffusion-driven, because water diffuses much faster than plants.