Fairy circles and their non-local stochastic instability

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.