Bifurcation analysis of a spatial vegetation model

Abstract

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.