Abstract:

The first aim of this talk 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. After having recalled the definition of a solution of canard type for two-dimensional singularly pertubed systems and the main statements of these methods the result, i.e. the computation of the bifurcation parameter value leading to a canard explosion in dimension two will be then exemplified with the classical Van der Pol oscillator. The second aim of this talk is to show that the condition for the generic existence of solutions of canards type for three-dimensional singularly pertubed systems can be found according to the Flow Curvature Method. Such a result will be then highlighted with two classical examples.