Singular perturbations and vanishing passage through a turning point |
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Authors: | P De Maesschalck F Dumortier |
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Institution: | Hasselt University, Campus Diepenbeek, Agoralaan gebouw D, B-3590 Diepenbeek, Belgium |
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Abstract: | The paper deals with planar slow-fast cycles containing a unique generic turning point. We address the question on how to study canard cycles when the slow dynamics can be singular at the turning point. We more precisely accept a generic saddle-node bifurcation to pass through the turning point. It reveals that in this case the slow divergence integral is no longer the good tool to use, but its derivative with respect to the layer variable still is. We provide general results as well as a number of applications. We show how to treat the open problems presented in Artés et al. (2009) 1] and Dumortier and Rousseau (2009) 13], dealing respectively with the graphics DI2a and DF1a from Dumortier et al. (1994) 14]. |
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Keywords: | 34E15 34C26 34E20 37G15 |
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