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Geometric singular perturbation analysis of an autocatalator model. (English) Zbl 1362.34076

Summary: 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.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C26 Relaxation oscillations for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
80A30 Chemical kinetics in thermodynamics and heat transfer
34C45 Invariant manifolds for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

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