An Iterative Method for the Approximation of Fibers in Slow-Fast Systems

Research output: Contribution to journalJournal articleResearchpeer-review

220 Downloads (Pure)

Abstract

In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite-dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers. The method is demonstrated on the Michaelis--Menten--Henri model and the Lindemann mechanism. The latter example also serves to demonstrate the method on a slow-fast system in nonstandard slow-fast form. Finally, we extend the method further so that it also approximates the curvature of the fibers.
Original languageEnglish
JournalS I A M Journal on Applied Dynamical Systems
Volume13
Issue number2
Pages (from-to)861–900
ISSN1536-0040
DOIs
Publication statusPublished - 2014

Keywords

  • Slow-fast systems
  • Singular perturbation theory
  • Reduction methods

Cite this