Slow Divergence Integral and Balanced Canard Solutions

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...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2011-04, Vol.10 (1), p.65-85
Main Author: Dumortier, Freddy
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-011-0038-9