https://doi.org/10.1140/epjst/e2016-60178-1
Regular Article
Fairy circles and their non-local stochastic instability
1 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico, 87501, USA IIF-Sadaf, Bulnes 642, 1428, Buenos Aires, Argentina
2 Facultad de Ingeniería y Tecnología, Universidad San Sebastián, Lota 2465, Santiago 7510157, Chile
3 Centro Atómico Bariloche (CNEA), Instituto Balseiro (Uni. Nac. Cuyo), and CONICET, Av. E. Bustillo 9500, CP 8400, Bariloche, Argentina
a e-mail: fuentesm@santafe.edu
Received: 10 June 2016
Revised: 26 September 2016
Published online: 6 March 2017
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.
© EDP Sciences, Springer-Verlag, 2017
