title: Localized vegetation patterns, fairy circles, and localized patches in arid landscapes.
abstract: We investigate the formation of localized structures with varying widths in one- and two-dimensional systems. The mechanism of stabilization is attributed to strongly nonlocal coupling mediated by a Lorentzian type of kernel. We show that, in addition to stable dips found recently [see, e.g. Fernandez-Oto et al., Phys. Rev. Lett. 110, 174101 (2013)], there are stable localized peaks which appear as a result of strongly nonlocal coupling. We applied this mechanism to arid ecosystems by considering a prototype model of a Nagumo type. In one dimension, we study the front connecting the stable uniformly vegetated state to the bare one under the effect of strongly nonlocal coupling. We show that strongly nonlocal coupling stabilizes both-dip and peak-localized structures. We show analytically and numerically that the width of a localized structure, which we interpret as a fairy circle, increases strongly with the aridity parameter. This prediction is in agreement with published observations. In addition, we predict that the width of localized patch decreases with the degree of aridity. Numerical results are in close agreement with analytical predictions.
authors.affiliation: Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12.455, Las Condes, Santiago, Chile.
authors.forename: D
authors.initials: D
authors.lastname: Escaff
authors.affiliation: Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), C.P. 231, Campus Plaine, B-1050 Bruxelles, Belgium.
authors.forename: C
authors.initials: C
authors.lastname: Fernandez-Oto
authors.affiliation: Departamento de Física, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile.
authors.forename: M G
authors.initials: MG
authors.lastname: Clerc
authors.affiliation: Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), C.P. 231, Campus Plaine, B-1050 Bruxelles, Belgium.
authors.forename: M
authors.initials: M
authors.lastname: Tlidi
mesh_terms: D003198:Computer Simulation; D017753:Ecosystem; D008954:Models, Biological; D009276:Namibia; D010944:Plants