Bifurcation and stability analysis of a cross‐diffusion vegetation‐water model with mixed delays

With desertification becoming more and more serious all over the world, it is crucial to understand the intrinsic relationship between vegetation and water (soil water and surface water). In this paper, a cross‐diffusion model with mixed delays is established to describe the dynamics of vegetation, soil water, and surface water in the case of water shortage. The local stability conditions of positive equilibrium point is established by using Routh–Hurwitz criterion. Then, the conditions for generating Hopf bifurcation are studied. In the end, numerical simulations are carried out to illustrate the effectiveness of the theoretical analysis.