Abstract

The aim of this work is to present the condition under which the Hindmarsh-Rose model exhibit canards solution. Such a model is a very particular and interesting case of three-dimensional singularly perturbed system involving two small multiplicative parameters in the left-hand-side of its velocity vector field.

Although, solutions of canard type have been predicted by Andrey Shilnikov (the son of the late Andrey Shilnikov), it does seem, to our knowledge, that conditions for the existence of such solutions have already been highlighted.

Joint work with Jaume Llibre and Kiyoyuki Tchizawa.