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The geometry of Wonderland |
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| Authors: | Eduard Gröller Rainer Wegenkittl Alexandra Milik Alexia Prskawetz Gustav Feichtinger Warren C Sanderson |
| Institution: | Institute of Computergraphics, Vienna University of Technology, Karlsplatz 13, 1040, Vienna, Austria Institute for Econometrics, Operations Research and Systems Theory, Vienna University of Technology, Karlsplatz 13, 1040, Vienna, Austria International Institute for Applied Systems Analysis, A-2361 Laxenburg and Department of Economics, State University of New York, Stony Brook, NY, USA |
| Abstract: | We analyze Wonderland—a model of demographic, economic and environmental interactions—by combining numerical simulations with basic ideas of geometric singular perturbation theory. This theory dealing with slow-fast dynamical systems helps us to gain new insights into the behaviour of the system. We give conditions for the occurrence of rapid environmental changes in Wonderland. Since the chosen approach is inherently geometric we also focus on the visualization of our results. |
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