## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Asymptotic study of planar canard solutions

Thomas Forget

#### 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

https://projecteuclid.org/euclid.bbms/1228486409

Digital Object Identifier
doi:10.36045/bbms/1228486409

Mathematical Reviews number (MathSciNet)
MR2484134

Zentralblatt MATH identifier
1189.34104

#### 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