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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
43/2009

Geometric singular perturbation analysis of an autocatalator model

Ilona Gucwa and Peter Szmolyan

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.

Received:
Jul 23, 2009
Published:
Jul 24, 2009
MSC Codes:
34C26, 34C30, 34C40, 34E15, 34E2, 37C10, 37C27
Keywords:
slow-fast system, geometric singular perturbation theory, slow manifolds, blow-up, relaxation oscillations

Related publications

inJournal
2009 Repository Open Access
Ilona Kosiuk and Peter Szmolyan

Geometric singular perturbation analysis of an autocatalator model

In: Discrete and continuous dynamical systems / S, 2 (2009) 4, pp. 783-806