Bifurcation and pattern formation in diffusive Klausmeier-Gray-Scott model of water-plant interaction

A reaction-diffusion model describing water and plant interaction proposed by Klausmeier is studied. The existence of non-constant steady state solutions shown through bifurcation methods, the large amplitude spatial patterned proved using associated shadow system. It rigorously that non-homogeneous vegetation states exist when rainfall at a lower level in which homogeneous cannot survive. Even very low, slow diffusion fast can support with concentrating on small area. This provides an example diffusion-induced persistence may system there are no positive constant states.