The mathematics of desertification: searching for early warning signals

Arjen Doelman (Universiteit Leiden)

Waaier 2, 12:15 - 13:00

The process of desertification can be modeled by systems of reaction-diffusion equations that describe the interactions between (ground)water and vegetation. Numerical simulations of these models agree remarkably well with field observations; both of these show that `vegetation patterns' -- i.e. regions in which the vegetation only survives in localized `patches' -- naturally appear as the transition between a healthy homogeneously vegetated state and the (non-vegetated) desert state. Desertification is a catastrophic and non-reversible event during which huge patterned vegetation areas `collapse' into the desert state at a fast time scale -- for instance as a consequence of a slow decrease of yearly rainfall, or through an increased grazing pressure. From the environmental point of view, it is crucial to be able to recognize whether or not a patterned state is close to collapse; ecologists are thus searching for `early warning signals'. In this talk, we will translate the issues raised by the desertification process into mathematical terms and relate these to very recent developments in the field of pattern formation. It will be shown that the process of desertification yields deep mathematical challenges and that these have already led to the development of novel mathematical theory.

Arjen Doelman (PhD 1990 at Utrecht University) has a full-time appointment at Leiden University, partly as professor at the Mathematical Institute and partly as director of the Lorentz Center.

His main research interests are in the fields of nonlinear dynamical systems, pattern formation, singular perturbation theory and their applications (in oceanography, geophysics, chemistry, hydrodynamics, ecology, biology). Arjen is Editor-in-Chief of Physica D and editor of the Journal on Computational Science.