English

Asymptotic expansion of planar canard solutions near a non-generic turning point

Dynamical Systems 2008-12-12 v1 Optimization and Control

Abstract

This paper deals with the asymptotic study of the so-called canard solutions, which arise in the study of real singularly perturbed ODEs. Starting near an attracting branch of the "slow curve", those solutions are crossing a turning point before following for a while a repelling branch of the "slow curve". Assuming that the turning point is degenerate (or non-generic), we apply a correspondence presented in a recent paper. This application needs the definition of a family of functions ϕ\phi that is studied in a first part. Then, we use the correspondence is used to compute the asymptotic expansion in the powers of the small parameter for the canard solution.

Keywords

Cite

@article{arxiv.0812.2226,
  title  = {Asymptotic expansion of planar canard solutions near a non-generic turning point},
  author = {Thomas Forget},
  journal= {arXiv preprint arXiv:0812.2226},
  year   = {2008}
}