THE DYNAMICS OF SLOW MANIFOLDS

Ferdinand Verhulst; Taoufik Bakri

doi:10.22342/jims.13.1.76.73-90

Ferdinand Verhulst ⁽¹⁾ , Taoufik Bakri ⁽²⁾

(1) Mathematisch Instituut, University of Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands., Netherlands,

(2) Mathematisch Instituut, University of Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands., Netherlands

https://doi.org/10.22342/jims.13.1.76.73-90

Issue
Volume 13 Number 1 (April 2007)

Submitted
May 25, 2012

Accepted
July 1, 2012

Published
July 1, 2012

Keywords:

singular perturbations, slow manifolds, periodic solutions, canards, relaxation oscillations

No galleys available

Abstract

After reviewing a number of results from geometric singular perturbation theory, we discuss several approaches to obtain periodic solutions in a slow manifold.Regarding nonhyperbolic transitions we consider relaxation oscillations and canard-like solutions. The results are illustrated by prey-predator systems.

DOI : http://dx.doi.org/10.22342/jims.13.1.76.73-90

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Authors

Ferdinand Verhulst

Mathematisch Instituut, University of Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands.

penulis@jims-a.org (Primary Contact)

Taoufik Bakri

Mathematisch Instituut, University of Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands.

Verhulst, F., & Bakri, T. (2012). THE DYNAMICS OF SLOW MANIFOLDS. Journal of the Indonesian Mathematical Society, 13(1), 73–90. https://doi.org/10.22342/jims.13.1.76.73-90