University of Heidelberg, Applied Analysis Seminar
Thu 05.12.2019
14:15, posted in Applied Analysis
Prof. Dr. Arjen Doelman (University of Leiden)
The interactions of singular patterns and the process of desertification
INF 205, SR1

Singular patterns appear in multi-scale systems. These systems exhibit the rich behavior of general systems, their singular nature provides a structure by which this may be understood. Moreover, many natural phenomena are modeled by such systems. Unravelling the nature of patterns exhibited by specific chemical or ecological models goes hand in hand with uncovering novel mathematical destabilization mechanisms as the Hopf dance. Understanding realistic patterns requires analytical descriptions of deformations, bifurcations and annihilation of interacting localized structures -- from an ecological point of view preferably under varying (climatological) circumstances: desertification can be seen, better: should be seen, as the coarsening process of a multi-pulse pattern induced by slowly varying parameters (that ends in the trivial `bare soil' state). By this point of view, the mathematical theory of singular pulse interactions may explain why desertification sometimes is a sudden catastrophic event, while it is a gradual process in other situations.

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