A Study Of Vegetation Patterns And Numerical Simulation In The Plain Desert Temperate Zone

In this thesis,we discussed the formation principle of vegetation pattern in the Plain Desert Temperate Zone and the relationship between the various influencing factors by using mathematical model.Based on previous models and related knowledge of ecology,the reaction-diffusion model corresponding to vegetation pattern is given.Firstly,We using upper and lower solutions method proved the local existence and uniqueness of solutions for a vegetation patterns model and discussed the non-negative equilibrium solutions of the differential system.Then,the mechanism of vegetation pattern formation is analyzed by using Turing bifurcation method,and the existence conditions of Turing pattern solution are obtained,and the existence conditions are verified by numerical experiments.Finally,two finite difference schemes for the reaction-diffusion model are given.The truncation error and stability of the difference scheme are analyzed.One-dimensional and twodimensional numerical simulations of the reaction-diffusion model are performed using the constructed finite difference method.in this thesis shows that the formation of vegetation patterns in temperate desert areas is caused by the diffusion of plants and water,and the limited water resources(precipitation)and feedback between plants are the final states affecting the evolution of vegetation.