Contributions to Books:
I. Gucwa, P. Szmolyan:
"Scaling in singular perturbation problems: blowing-up a relaxation oscillator";
in: "ASC Report 39/2009",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
An introduction to some recently developed methods for the analysis of systems
of singularly perturbed ordinary di«erential equations is given in the context of a speci»c problem
describing glycolytic oscillations. In suitably scaled variables the governing equations are a planar
system of ordinary di«erential equations depending singularly on two small parameters " and ▒. In
 it was argued that a limit cycle of relaxation type exists for " ┐ ▒ ┐ 1. The existence of this
limit cycle is proven by analyzing the problem in the spirit of geometric singular perturbation theory.
The degeneracies of the limiting problem corresponding to ("; ▒) = (0; 0) are resolved by repeatedly
applying the blow-up method. It is shown that the blow-up method leads to a clear geometric picture
of this fairly complicated two parameter multi-scale problem.
slow-fast dynamics, relaxation oscillations, geometric singular perturbation theory,
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.