Geometric singular perturbation analysis
of an autocatalator model

Ilona Gucwa, and Peter Szmolyan
(Please use for correspondence this email).

Submission date: 23. Jul. 2009
Pages: 25
paper accepted for publication in: Discrete and Continuous Dynamical Systems Series S
MSC-Numbers: 34C26, 34C30, 34C40, 34E15, 34E2, 37C10, 37C27
Keywords and phrases: slow-fast system, geometric singular perturbation theory, slow manifolds, blow-up, relaxation oscillations
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Abstract:
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.