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December 2008 Asymptotic study of planar canard solutions
Thomas Forget
Bull. Belg. Math. Soc. Simon Stevin 15(5): 809-824 (December 2008). DOI: 10.36045/bbms/1228486409

Abstract

We are interested in the asymptotic study of canard solutions in real singularly perturbed first order ODE of the form $\varepsilon u'=\Psi(x,u,a,\varepsilon)$, where $\varepsilon>0$ is a small parameter, and $a\in\mathbb R$ is a real control parameter. An operator $\Xi_\eta$ was defined to prove the existence of canard solutions. This demonstration allows us to conjecture the existence of a generalized asymptotic expansion in fractional powers of $\varepsilon$ for those solutions. In this note, we propose an algorithm that computes such an asymptotic expansions for the canard solution. Furthermore, those asymptotic expansions remain uniformly valid.

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Thomas Forget. "Asymptotic study of planar canard solutions." Bull. Belg. Math. Soc. Simon Stevin 15 (5) 809 - 824, December 2008. https://doi.org/10.36045/bbms/1228486409

Information

Published: December 2008
First available in Project Euclid: 5 December 2008

zbMATH: 1189.34104
MathSciNet: MR2484134
Digital Object Identifier: 10.36045/bbms/1228486409

Subjects:
Primary: 34E05, 34E10, 34E20

Rights: Copyright © 2008 The Belgian Mathematical Society

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Vol.15 • No. 5 • December 2008
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