Fig. 4. Theoretical modeling of the dislocation decay law: Numerical simulations for three models of migrating banded vegetation patterns with different advection parameters.

(A and B) correspond to the integrodifferential model Eq. 1. Parameters are l_fx = l_fy = 0.5, l_cx = 2.2, l_cy = 0.3, μ = 0.95, χ_f = 2.8, χ_c = 2.0, d = 0.01, for (A) x_0f = −0.2 and x_0c = 0.1, for (B) x_0f = −0.4 and x_0c = 0.8. (C and D) show the weak gradient model Eq. 2, parameters are η = −0.04, κ = 0.3, p = 0.05, γ = 1.9, for (C) α = 0.4, for (D) α = 1.0. (E and F) represent the water-biomass model (3), parameters are γ = 2.0, σ = 1.5, d = 0.1, μ = 0.1, w₀ = 0.3, ρ = 0, β = 0, v = 4.0, for (E) α = −1.4, for (F) α = −2.0. The right panels correspond to the respective number of dislocations N(x) as a function of the propagation coordinate (x/λ) for each model in the regime of asymptotic uniform stripe patterns. Fit parameters in λ units are (G) x₀ = 27.2, B = 4.1, and A = 0.2 (R² = 0.99); (H) x₀ = −7, B = 3.8, and A = 0.5 (R² = 1.0); (I) x₀ = 14.3, B = 0.7, and A = 0.06 (R² = 0.99).