Geometric singular perturbation analysis of an autocatalator model

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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

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

Abstract
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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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