Geometric singular perturbation analysis of an autocatalator model
Ilona Gucwa and Peter Szmolyan
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Submission date: 23. Jul. 2009
published in: Discrete and continuous dynamical systems / S, 2 (2009) 4, p. 783-806
DOI number (of the published article): 10.3934/dcdss.2009.2.783
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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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.