Localized vegetation patterns, fairy circles, and localized patches in arid landscapes

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D EscaffM Tlidi

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.

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Citations

Oct 29, 2015·PloS One·Walter R Tschinkel
Jul 5, 2012·PloS One·Walter R Tschinkel
Sep 22, 2016·Scientific Reports·Ignacio BordeuMustapha Tlidi
May 8, 2016·Physical Review Letters·F MaucherW Krolikowski
Jul 25, 2019·Physical Review. E·V DornelasC Anteneodo
Mar 17, 2017·Physical Review. E·P Parra-RivasD Gomila
Feb 16, 2019·Physical Review Letters·Cristian Fernandez-OtoEhud Meron
Oct 30, 2015·Bulletin of Mathematical Biology·Canrong Tian
Aug 5, 2017·Physical Review Letters·J JavaloyesM Giudici
Jun 25, 2020·Physical Review. E·P Parra-Rivas, C Fernandez-Oto
Apr 19, 2017·Physical Review. E·Alexandre RosasKatja Lindenberg
Aug 3, 2018·Chaos·Daniel EscaffKatja Lindenberg
Aug 3, 2021·Physics of Life Reviews· InderjitEhud Meron

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