Multiple Time Scales and Canards in a Chemical Oscillator

  • Alexandra Milik
  • Peter Szmolyan
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 122)


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 fibers in a region relevant to the dynamics. Thus normal hyperbolicity of the critical manifold is lost in two regions. The dynamics depends crucially on effects 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.

Key words

Geometric singular perturbation theory chemical oscillator canard solutions blow-up 


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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Alexandra Milik
    • 1
    • 2
  • Peter Szmolyan
    • 1
  1. 1.Institut für Angewandte und Numerische MathematikTechnische Universität WienViennaAustria
  2. 2.IMAUniversity of MinnesotaUSA

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