Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. V: The transition from patterns to desert (Q2862269)

In this paper, a system of reaction-diffusion-advection equations involving the plant density and water density is considered. A very large dimensionless parameter (called the slope gradient) is studied, that reflects the relative rates of water flow downhill and plant dispersal. The author's concern is the existence and form of periodic travelling waves of the Klausmeier model, to leading order as the slope gradient tends to infinity, provided that the migration speed scales with the slope gradient in given ways. A~detailed numerical study of the existence and stability of periodic traveling waves is done via numerical procedures. The author shows via numerical simulations that a decrease in rainfall through the minimum level for patterns causes a transition to full-blown desert that cannot be reversed by increasing the rainfall again. The author includes a summary of the work done in his previous four papers on the Klausmeier model, as this is the last one of the series.NEWLINENEWLINEFor Part IV see [the author, ibid. 73, No. 1, 330--350 (2013; Zbl 1321.92083)].