## Information

- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: August 1997
- Number: TR-186-2-97-14
- Keywords:

## Abstract

We present a geometric explanation of a basic mechanism
generating mixed-mode oscillations in a prototypical simple
model of a chemical oscillator. Our approach is based on
geometric singular perturbation theory and canard solutions. We
explain how the small oscillations are generated near a special
point, which is classified as a folded saddle-node for the
reduced problem. The canard solution passing through this point
separates small oscillations from large relaxation type
oscillations. This allows to define a one-dimensional return
map in a natural way. This bimodal map is capable of
explaining the observed bifurcation sequence convincingly.

## Additional Files and Images

## Weblinks

No further information available.

## BibTeX

@techreport{Milik-1997-GMMO,
title = "Geometry of Mixed-mode Oscillations in the 3-d
Autocatalator",
author = "Alexandra Milik and Peter Szmolyan and Helwig L\"{o}ffelmann
and Eduard Gr\"{o}ller",
year = "1997",
abstract = "We present a geometric explanation of a basic mechanism
generating mixed-mode oscillations in a prototypical simple
model of a chemical oscillator. Our approach is based on
geometric singular perturbation theory and canard solutions.
We explain how the small oscillations are generated near a
special point, which is classified as a folded saddle-node
for the reduced problem. The canard solution passing
through this point separates small oscillations from large
relaxation type oscillations. This allows to define a
one-dimensional return map in a natural way. This bimodal
map is capable of explaining the observed bifurcation
sequence convincingly.",
month = aug,
number = "TR-186-2-97-14",
address = "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
institution = "Institute of Computer Graphics and Algorithms, Vienna
University of Technology ",
note = "human contact: technical-report@cg.tuwien.ac.at",
URL = "https://www.cg.tuwien.ac.at/research/publications/1997/Milik-1997-GMMO/",
}