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

D. Escaff, C. Fernandez-Oto, M. G. Clerc, M. Tlidi

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


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, Phys. Rev. Lett. 110, 174101 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.174101], 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.

Original languageEnglish
Article number022924
JournalPhysical Review E
Issue number2
StatePublished - 26 Feb 2015

Bibliographical note

Publisher Copyright:
© 2015 American Physical Society.


  • Computer Simulation
  • Ecosystem
  • Models, Biological
  • Namibia
  • Plants


Dive into the research topics of 'Localized vegetation patterns, fairy circles, and localized patches in arid landscapes'. Together they form a unique fingerprint.

Cite this