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December  2009, 2(4): 783-806. doi: 10.3934/dcdss.2009.2.783

Geometric singular perturbation analysis of an autocatalator model

Ilona Gucwa 1, and  Peter Szmolyan 2,

1. 

Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig, Germany
2. 

Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria

Received  September 2008 Revised  April 2009 Published  September 2009

A singularly perturbed planar system of differential equations modeling an autocatalytic chemical reaction is studied. For certain parameter values a limit cycle exists. Geometric singular perturbation theory is used to prove the existence of this limit cycle. A central tool in the analysis is the blow-up method which allows the identification of a complicated singular cycle which is shown to persist.
Keywords: relaxation oscillations., slow manifolds, slow-fast system, geometric singular perturbation theory, blow-up.
Mathematics Subject Classification: Primary: 34C26, 34C30, 34C40, 34E15, 34E20, 37C10, 37C2.
Citation: Ilona Gucwa, Peter Szmolyan. Geometric singular perturbation analysis of an autocatalator model. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : 783-806. doi: 10.3934/dcdss.2009.2.783
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