Stability and vegetation patterns driven by both nonlocal infiltration and nonlocal absorption in the extended Klausmeier model

Abstract

In this paper, we propose a dryland ecosystem model with both nonlocal infiltration and nonlocal absorption and investigate the influence of the nonlocal effect on the vegetation patterns. For the local model, the existence and stability of the nonnegative equilibria are theoretically investigated. For the diffusive model without nonlocal effect, diffusion-driven Turing instability and the critical value of the diffusion coefficient are determined. For the diffusive model with nonlocal effects characterized by the spatial average kernel, the mode-1 steady state bifurcation occurs. For the diffusive model with nonlocal effects characterized by the top-hat kernel, it has been shown that a transition of vegetation patterns occurs when the scale of nonlocal infiltration and nonlocal absorption varies.