Flow Curvature Method applied to Canard Explosion

Jean-Marc Ginoux (1) , Jaume Llibre (2)

1 PROTEE - Processus de Transfert et d'Echanges dans l'Environnement - EA 3819
2 UAB - Departament de Matemàtiques [Barcelona]

The aim of this work is to establish that the bifurcation parameter value leading to a canard explosion in dimension two obtained by the so-called Geometric Singular Perturbation Method can be found according to the Flow Curvature Method. This result will be then exemplified with the classical Van der Pol oscillator.

Keywords: Geometric Singular Perturbation Method; Flow Curvature Method; singularly perturbed dynamical systems; canard solutions

Domains: Dynamical Systems [math.DS]

Jean-Marc Ginoux, Jaume Llibre. Flow Curvature Method applied to Canard Explosion. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011, 44 (46), pp.465203. ⟨10.1088/1751-8113/44/46/465203⟩. ⟨hal-01056936⟩