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Geometric singular perturbation analysis of an autocatalator model
Ilona Gucwa and Peter SzmolyanAbstract
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:
- 23.07.09
- Published:
- 24.07.09
- MSC Codes:
- 34C26, 34C30, 34C40, 34E15, 34E2, 37C10, 37C27
- Keywords:
- slow-fast system, geometric singular perturbation theory, slow manifolds, blow-up, relaxation oscillations