VEGETATION PATTERN FORMATION IN A SEMI-ARID CLIMATE

A partial bifurcation diagram of a reaction-diffusion type model of two-dimensional vegetation patterns in a semi-arid climate is computed using numerical continuation techniques. In previous studies with this model, it has been shown that two positive feedbacks (the infiltration feedback and precipitation feedback) may influence the type of vegetation patterns which appear under a certain precipitation forcing. In this bifurcation study, first the case is considered where the infiltration feedback is the only positive feedback. The partial bifurcation diagram of the different steady states is more complicated than earlier model results have suggested and provides insight into how the pattern selection process takes place. Finally, it is shown that when the precipitation feedback is included, the bifurcation diagram is only shifted to smaller precipitation values.