Canard explosion in delayed equations with multiple timescales
Dynamical Systems
2014-07-30 v1
Abstract
We analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast system with delayed self-coupling. In the absence of delays, this system provides a canonical example of a canard explosion. We show that as the delay is increased a family of `classical' canard explosions ends as a Bogdanov-Takens bifurcation occurs at the folds points of the S-shaped critical manifold.
Cite
@article{arxiv.1407.7703,
title = {Canard explosion in delayed equations with multiple timescales},
author = {Maciej Krupa and Jonathan D. Touboul},
journal= {arXiv preprint arXiv:1407.7703},
year = {2014}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1404.5841