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Vegetation pattern formation in a semi-arid climate. (English) Zbl 1270.35087

Summary: 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.

MSC:

35B36 Pattern formations in context of PDEs
35B32 Bifurcations in context of PDEs
65P30 Numerical bifurcation problems
86A10 Meteorology and atmospheric physics
35K57 Reaction-diffusion equations
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