Flow Curvature Method applied to Canard Explosion

TL;DR

This paper demonstrates that the Flow Curvature Method can identify the bifurcation parameter for canard explosions in two-dimensional systems, aligning with results from the Geometric Singular Perturbation Method, exemplified through the Van der Pol oscillator.

Contribution

It establishes a link between the Flow Curvature Method and the Geometric Singular Perturbation Method for locating canard explosion bifurcations in 2D systems.

Findings

Flow Curvature Method accurately predicts bifurcation parameters.

Validation with the Van der Pol oscillator confirms the method's effectiveness.

Provides a new approach for analyzing canard phenomena in dynamical systems.

Abstract

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.