Abstract
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains and explores geometric singular perturbation theory and its use in (biological) practice. The three main theorems due to Fenichel are the fundamental tools in the analysis, so the strategy is to state these theorems and explain their significance and applications. The theory is illustrated by many examples.
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Acknowledgments
This work was supported by NWO grant MEERVOUD 632000.002, and very much stimulated by Odo Diekmann.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hek, G. Geometric singular perturbation theory in biological practice. J. Math. Biol. 60, 347–386 (2010). https://doi.org/10.1007/s00285-009-0266-7
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DOI: https://doi.org/10.1007/s00285-009-0266-7