2015/07/31 by Karna Gowda, Yuxin Chen, Sarah Iams +1 · 1 citation
Physics and Astronomy · #nlin.PS
paper · pdf · doi:10.1098/rspa.2015.0893
published as Proceedings of the Royal Society A , Vol. 472, 20150893, 2016 · Main text: 27 pages, 8 figures, 2 tables. Supplementary information: 3 pages, 1 figure
arxiv created 2016/02/23 · arxiv updated 2016/03/31
A particular sequence of patterns, "gaps → labyrinth → spots," occurs with decreasing precipitation in previously reported numerical simulations of PDE dryland vegetation models. These observations have led to the suggestion that this sequence of patterns can serve as an early indicator of desertification in some ecosystems. Since parameter values can take on a range of plausible values in the vegetation models, it is important to investigate whether the pattern sequence prediction is robust to variation. For a particular model, we find that a quantity calculated via bifurcation-theoretic analysis appears to serve as a proxy for the pattern sequences that occur in numerical simulations across a range of parameter values. We find in further analysis that the quantity takes on values consistent with the standard sequence in an ecologically relevant limit of the model parameter values. This suggests that the standard sequence is a robust prediction of the model, and we conclude by proposing a methodology for assessing the robustness of the standard sequence in other models and formulations.