Traveling Stripes in the Klausmeier Model of Vegetation Pattern Formation

DOI10.1137/18M1196996zbMath1403.35132WikidataQ128870833 ScholiaQ128870833MaRDI QIDQ4558782

Paul Carter, Arjen Doelman

Publication date: 30 November 2018

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

pattern formationtraveling wavesgeometric singular perturbation theoryblow-up desingularizationreaction diffusion advection equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Ecology (92D40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07) Pattern formations in context of PDEs (35B36)

Related Items (8)

Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains ⋮ The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation ⋮ Slow localized patterns in singularly perturbed two-component reaction–diffusion equations ⋮ Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization ⋮ Large amplitude radially symmetric spots and gaps in a dryland ecosystem model ⋮ Turing instability and coexistence in an extended Klausmeier model with nonlocal grazing ⋮ Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems ⋮ Analysis of Spot Patterns on a Coordinate-Invariant Model for Vegetation on a Curved Terrain

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