A Mathematical Study Of Vegetation And Desertification Models

The study of vegetation and desertification model has certain significance to the prevention and control of soil desertification,so the study of vegetation and desertification model has become one of the important topics in the field of eco-logical environment.In this paper,on the basis of the existing vegetation pattern model,we introduce the cross-diffusion term and improve the model by considering the influence of plant roots absorbing water from the soil.Firstly,the existence and uniqueness of the solution of the model are analyzed by using the theoretical knowl-edge of partial differential equations,and then the stability of the non-negative equilibrium point of the differential equation is discussed.In the last numerical simulation,we use explicit difference scheme and Crank-Nicolson difference scheme to simulate one dimension and two dimension problems respectively,and get the corresponding results.