Pattern dynamics of vegetation and soil nutrients in eroded areas

In this paper, we focus on erosion areas with severe soil degradation, where vegetation self-organizes to form different landscape patterns under resource constraints. Considering the interaction between soil nutrients and vegetation biomass, we use a discrete advection–reaction–diffusion equation to model the vegetation–nutrient dynamic system. Specifically, we refine the typical Klausmeier model to a spatiotemporal discrete difference equation and use advection terms to capture dynamic information about the movement of soil material with surface runoff. By analyzing the weak stability of the model’s Turing condition and Neimark–Sacker condition, we find that when the soil nutrient content drops to a critical value, the system undergoes Turing instability and Neimark–Sacker bifurcation, accompanied by specific vegetation patterns. In addition, during the numerical simulation, Shannon entropy and contagion index are introduced as landscape indicators to quantify the diversity and connectivity of vegetation spatial patterns. Results indicate that an increase in the diffusion effect is more conducive to the emergence of Turing vegetation patterns.