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# Mathematics of desertification

For fans of dynamical systems theory, I recently attended a seminar on "The Mathematics of Desertification" by Arjen Doelman of Leiden University, discussing work in a recent paper.

To summarize, he's interested in modeling the spatial dynamics of vegetation patterns in desert areas using nonlinear reaction-diffusion equations. These equations can show threshold collapse behavior, where variations in grazing or precipitation can lead to an abrupt and (nearly) irreversible disappearance of vegetation, i.e. total desertification. He would like to identify early warning signals of an impending collapse. Unfortunately he has not yet progressed to finding such indicators, but he did lots of math to characterize the system dynamics.

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Neat stuff!

Comment Source:Neat stuff!
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edited November 2011

Hmm! By the way, someone just pointed out that the greening of parts of the Sahara is listed on this map of Tipping elements:

Our page should discuss this, but it doesn't yet!

Did Doelman talk at all about 'de-desertification'?

Comment Source:Hmm! By the way, someone just pointed out that the _greening_ of parts of the Sahara is listed on this map of [[Tipping points|Tipping elements]]: <a href = "http://www.pnas.org/content/105/6/1786.long"><img width = "700" src = "http://www.pnas.org/content/105/6/1786/F1.large.jpg" alt = ""/></a> * T. M. Lenton, H. Held, E. Kriegler, J. W. Hall, W. Lucht, S. Rahmstorf, and H. J. Schellnhuber, [Tipping elements in the Earth's climate system](http://www.pnas.org/content/105/6/1786.long), _Proceedings of the National Academy of Sciences_ **105** (Feb 2008). Our page should discuss this, but it doesn't yet! Did Doelman talk at all about 'de-desertification'?
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All Doelman said about "de-desertification" is that in his model, once you reach a desert state it's hard to get out of it without very high increases in precipitation. I don't think he'd focused too closely on quantifying this with real-world numbers.

Comment Source:All Doelman said about "de-desertification" is that in his model, once you reach a desert state it's hard to get out of it without very high increases in precipitation. I don't think he'd focused too closely on quantifying this with real-world numbers.
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should i add it to the Reaction diffusion equation page?

Comment Source:should i add it to the [[Reaction diffusion equation]] page?
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Sure!

Comment Source:Sure!