Gucwa, Ilona; Szmolyan, Peter Geometric singular perturbation analysis of an autocatalator model. (English) Zbl 1362.34076 Discrete Contin. Dyn. Syst., Ser. S 2, No. 4, 783-806 (2009). 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. Cited in 1 ReviewCited in 33 Documents 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 Keywords:slow-fast system; geometric singular perturbation theory; slow manifolds; blow-up; relaxation oscillations Software:XPPAUT PDFBibTeX XMLCite \textit{I. Gucwa} and \textit{P. Szmolyan}, Discrete Contin. Dyn. Syst., Ser. S 2, No. 4, 783--806 (2009; Zbl 1362.34076) Full Text: DOI