Scaling invariant interpolation for singularly perturbed vector fields (SPVF)

Viatcheslav Bykov, Vladimir Gol'Dshtein, Ulrich Maas

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


The problem of modelling, numerical simulations and interpretation of the simulations results of complex systems arising in reacting flows requires more and more sophisticated methods of qualitative system analysis. Recently, the concept of invariant, slow/fast, attractive manifolds has proven to be an efficient tool for such an analysis. In particular, it allows us to study main properties of detailed models describing the reacting flow by considering appropriate low dimensional manifolds, which appear naturally in the system state/composition space as a manifestation of a restricted number of real degrees of freedom exhibited by the system.In order to answer the question of what are the minimal number of the real degrees of freedom (real system dimension) and to approximate low dimensional manifolds (i.e., reduced system's phase spaces) the concept of Singularly Perturbed Vector Fields (SPVF) has been suggested lately [1]. In the current work a scales invariant version of the SPVF will be presented and discussed.

Original languageEnglish
Title of host publicationCoping with Complexity
Subtitle of host publicationModel Reduction and Data Analysis
Number of pages21
StatePublished - 1 Jan 2011
EventInternational Research Workshop: Coping with Complexity: Model Reduction and Data Analysis - Ambleside, United Kingdom
Duration: 31 Aug 20094 Sep 2009

Publication series

NameLecture Notes in Computational Science and Engineering
Volume75 LNCSE
ISSN (Print)1439-7358


ConferenceInternational Research Workshop: Coping with Complexity: Model Reduction and Data Analysis
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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