Slow-fast Dynamics in Wonderland

Taking Wonderland -- a simple model of demographic, economic, and environmental interactions -- as our artificial world, we illustrate the use of geometric singular perturbation theory in environmental demoeconomics. The theory of slow-fast dynamics helps us to gain new insights into the systems behavior and allows us one to reduce the inherent unpredictability of a "natural catastrophe" in Wonderland. Though we cannot predict the exact date of such an "environmental crash," we can state the specific demographic, economic and environmental constellations of our artificial world at which the sustainability of nature becomes endangered.

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