The vegetative cover in semi-arid landscape typically occurs as patches of individual species more or less separated from one another by bare ground. Klausmeier (1999) reported that the vegetation striped patterns grow lying along the contours of gentle slopes. He proposed a model of vegetation stripes based on competition for water. In this study, we mainly look into the positive feedback effects between the water and biomass on the vegetation spatial pattern formation within the non-saturated soil, which arises from the suction of water by the roots and processes of water resource redistribution. We use numerical calculations to obtain the dispersion relation, and study the effect of positive feedback function on the dispersion function such as the changes of the wavelength, wave speed as well as the conditions of the spatial pattern formation.
Results/Conclusions
Our results show that the trees are more sensitive than grasses to the positive feedback function to form a spatial pattern, and the stronger positive feedback increase the parameters’ region where vegetation bands occur, which indicates that the positive feedback raises the possibility of ecological shifts from green to desert states in semi-arid areas. Our numerical results also show that the positive feedback can increase the moving speed of the vegetation stripes.