Abstract:

A vegetation-water reaction-diffusion model with shading effect under no-flux boundary conditions is studied. The existence of steady-state bifurcation of the model is firstly proved, and the conditions for the generation of steady-state bifurcation are obtained. Then the structure of the non-constant steady-state solution in the case of single eigenvalues is obtained by using the Crandall-Rabinowitz bifurcation theorem. By adopting the implicit function theorem and the techniques of space decomposition, the structure of the non-constant steady-state solution in the case of double eigenvalues is obtained. Finally, numerical simulations are shown to verify the theoretical analysis results.

Key words: vegetation model, steady-state bifurcation, space decomposition, non-constant solutions