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

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 (β) and vegetation internal competition (σ) on pattern formation. Extending the Klausmeier framework, we integrate a cross-diffusion term Δ(w−βn) for root-driven soil–water feedback and a density-dependent competition term 1+σn2. Key findings include: (1) Increasing β drives sequential transitions from homogeneous states to gap, stripe, and spot patterns, while rising σ 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.