Dijkstra, Henk A. Vegetation pattern formation in a semi-arid climate. (English) Zbl 1270.35087 Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 12, 3497-3509 (2011). 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. Cited in 4 Documents 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 Keywords:bifurcation analysis; pattern formation; climate-biosphere interaction PDFBibTeX XMLCite \textit{H. A. Dijkstra}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 12, 3497--3509 (2011; Zbl 1270.35087) Full Text: DOI References: [1] DOI: 10.1126/science.1163381 · doi:10.1126/science.1163381 [2] DOI: 10.1007/s003820050164 · doi:10.1007/s003820050164 [3] DOI: 10.1111/j.1365-2486.2007.01327.x · doi:10.1111/j.1365-2486.2007.01327.x [4] Gilad E., Phys. Rev. Lett. pp 0981051– [5] DOI: 10.1016/j.jtbi.2006.08.006 · doi:10.1016/j.jtbi.2006.08.006 [6] DOI: 10.1016/j.tpb.2006.09.003 · Zbl 1124.92048 · doi:10.1016/j.tpb.2006.09.003 [7] Keller H. B., Applications of Bifurcation Theory (1977) [8] DOI: 10.1126/science.284.5421.1826 · doi:10.1126/science.284.5421.1826 [9] DOI: 10.1126/science.1154913 · doi:10.1126/science.1154913 [10] DOI: 10.1137/1027002 · Zbl 0576.92008 · doi:10.1137/1027002 [11] DOI: 10.1016/S0960-0779(03)00049-3 · Zbl 1083.92039 · doi:10.1016/S0960-0779(03)00049-3 [12] DOI: 10.1086/342078 · doi:10.1086/342078 [13] DOI: 10.1016/j.tree.2007.10.013 · doi:10.1016/j.tree.2007.10.013 [14] Sleijpen G. L. G., SIAM J. Matrix Anal. Appl. 17 pp 410– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.