Synergistic effects of feedback regulation and vegetation internal competition on vegetation patterns in semi-arid environments

Abstract

Against the backdrop of global aridification, the spatial self-organization of vegetation in semi-arid regions is critical to ecosystem stability. This study employs mathematical modeling to unravel the synergistic effects of soil–water diffusion feedback ($\beta$) and vegetation internal competition ($\sigma$) on pattern formation. Extending the Klausmeier framework, we integrate a cross-diffusion term $\Delta (w-\beta n)$ for root-driven soil–water feedback and a density-dependent competition term $1+\sigma n^2$. Key findings include: (1) Increasing $\beta$ drives sequential transitions from homogeneous states to gap, stripe, and spot patterns, while rising $\sigma$ induces reverse transitions, revealing their antagonistic roles in stability; (2) Enhanced precipitation promotes the expansion of discrete spots into continuous stripes, eventually forming gaps under water surplus. Root-mediated water uptake balances short-term facilitation and long-term competition, explaining adaptive responses to resource constraints. Spot patterns act as desertification warnings, whereas stripes offer restoration strategies via high water-use efficiency. By merging cross-diffusion and competition mechanisms, this work proposes a theoretical framework for arid land management, linking mechanistic insights to practical solutions against land degradation.