An iterative method for the canard explosion in general planar systems
Abstract
The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls the slow/fast dynamics. However, canard explosions are also observed in systems where no such parameter is present. Here we show how the iterative method of Roussel and Fraser, devised to construct regular slow manifolds, can be used to determine a canard point in a general planar system of nonlinear ODEs. We demonstrate the method on the van der Pol equation, showing that the asymptotics of the method is correct, and on a templator model for a self-replicating system.
Keywords
Cite
@article{arxiv.1209.1109,
title = {An iterative method for the canard explosion in general planar systems},
author = {Morten Brøns},
journal= {arXiv preprint arXiv:1209.1109},
year = {2012}
}
Comments
Paper presented at the 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA July 1 - 5, 2012