Vegetation pattern can describe spatial feature of vegetation in arid ecosystem. Soil-water diffusion is of vital importance in spatial structures of vegetation, which is not comprehensively understood. In this thesis, we reveal the impact of soil-water diffusion on vegetation patterns through steady-state bifurcation analysis. The result indicates that if soil-water diffusion coefficient is appropriately large, there is at least one non-constant steady-state solution to a spatial vegetation system. Moreover, with the aid of Crandall-Rabinowitz bifurcation theorem and implicit function theorem, local structure of non-constant steady-state solutions is obtained. Subsequently, the global continuation of the local steady-state bifurcation is performed, and we get global structure of non-constant solution. At last, the above non-constant steady-state solution is illustrated by our numerical simulations. The extended simulation additionally shows that the spatial heterogeneity of species is enhanced gradually as soil-water diffusion increases.

植被格局可以描述干旱生态系统植被的空间特征。水土扩散在植被空间结构中具有重要意义，但尚未得到全面认识。在本论文中，我们通过稳态分岔分析揭示了水土扩散对植被格局的影响。结果表明，如果土水扩散系数适当大，则空间植被系统至少存在一个非常量稳态解。此外，借助Crandall-Rabinowitz分岔定理和隐函数定理，得到了非常数稳态解的局部结构。随后，对局部稳态分岔进行全局延拓，得到非常数解的全局结构。最后，我们的数值模拟说明了上述非常量稳态解。扩展模拟还表明，随着土壤-水扩散的增加​​，物种的空间异质性逐渐增强。