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Slow Divergence Integral and Balanced Canard Solutions

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Abstract

The paper deals with smooth two-dimensional singular perturbation problems. Attention goes to the entry–exit relation for a generic Hopf- or jump breaking mechanism. We introduce the notions of balanced canard solution, slow relation and fast relation function. We show the role of these functions in the creation of relaxation oscillations and related bifurcations patterns, not only in the presence of a generic breaking parameter but also in the absence of such parameter.

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Authors and Affiliations

  1. Hasselt University, Campus Diepenbeek, Agoralaan, Gebouw D, 3590, Diepenbeek, Belgium

    Freddy Dumortier

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  1. Freddy Dumortier
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Correspondence to Freddy Dumortier.

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This work was completed with the support of our TEX-pert.

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Dumortier, F. Slow Divergence Integral and Balanced Canard Solutions. Qual. Theory Dyn. Syst. 10, 65–85 (2011). https://doi.org/10.1007/s12346-011-0038-9

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  • DOI: https://doi.org/10.1007/s12346-011-0038-9

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