Multiple Time Scales and Canards in a Chemical Oscillator

We present a geometric singular perturbation analysis of a chemical oscillator. Although the studied three-dimensional model is rather simple its dynamics are quite complex. In the original scaling the problem has a folded critical manifold which additionally becomes tangent to the fast bers in a region relevant to the dynamics. Thus normal hyperbolicity of the critical manifold is lost in two regions. The dynamics depends crucially on eeects due to the loss of normal hyperbolicity. In particular canard solutions play an essential role. We outline how rescalings and blow-up techniques can be used to prove the existence of canards in this problem and to explain other qualitative aspects of the dynamics.