Positive steady-state solutions for a water-vegetation model with the infiltration feedback effect

In this paper, a water-vegetation model with the infiltration feedback effect is considered. Firstly, through linear stability analysis, we get parameter area where Turing instability can occur. Next, by maximum principle, priori estimates for positive steady-state solutions are obtained and sufficient conditions nonexistence of nonconstant solution given. Moreover, bifurcations at both simple double eigenvalues analyzed separately. We establish global structure bifurcation from condition to determine direction. For case eigenvalues, techniques space decomposition implicit function theorem used. Finally, verify supplement theoretical analysis results numerical simulations.