The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 443–453

Fairy circles and their non-local stochastic instability

Regular Article

DOI: 10.1140/epjst/e2016-60178-1

Cite this article as:
Fuentes, M.A. & Cáceres, M.O. Eur. Phys. J. Spec. Top. (2017) 226: 443. doi:10.1140/epjst/e2016-60178-1
Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics

Abstract

We study analytically a non local stochastic partial differential equation describing a fundamental mechanism for patterns formation, as the one responsible for the so called fairy circles appearing in two different bio-physical scenarios; one on the African continent and another in Australia. Using a stochastic multiscale perturbation expansion, and a minimum coupling approximation we are able to describe the life-times associated to the stochastic evolution from an unstable uniform state to a patterned one. In this way we discuss how two different biological mechanisms can be collapsed in one analytical framework.

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico, 87501, USA IIF-Sadaf, Bulnes 642, 1428Buenos AiresArgentina
  2. 2.Facultad de Ingeniería y Tecnología, Universidad San SebastiánSantiago 7510157Chile
  3. 3.Centro Atómico Bariloche (CNEA), Instituto Balseiro (Uni. Nac. Cuyo), and CONICETBarilocheArgentina