Bulletin of the Belgian Mathematical Society - Simon Stevin

Asymptotic study of planar canard solutions

Thomas Forget

Full-text: Open access

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 5 (2008), 809-824.

Dates
First available in Project Euclid: 5 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1228486409

Digital Object Identifier
doi:10.36045/bbms/1228486409

Mathematical Reviews number (MathSciNet)
MR2484134

Zentralblatt MATH identifier
1189.34104

Subjects
Primary: 34E05: Asymptotic expansions 34E10: Perturbations, asymptotics 34E20: Singular perturbations, turning point theory, WKB methods

Keywords
Asymptotic expansions Asymptotics Singular perturbation Turning point theory

Citation

Forget, Thomas. Asymptotic study of planar canard solutions. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 5, 809--824. doi:10.36045/bbms/1228486409. https://projecteuclid.org/euclid.bbms/1228486409


Export citation