Bifurcation theory and computer algebra: An initial approach

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

Bifurcation theory studies the behavior of multiple solutions of nonlinear (differential) equations when parameters in these equations are varied, and describes how the number and type of these solutions change. It is a domain of applied mathematics which uses concepts from such diverse fields as functional analysis, group representations, ideal theory and many others. For real, e.g. physically motivated problems, the calculations necessary to determine even the simplest bifurcations become excessively complicated. Therefore, a project to build a package “bifurcation and singularity theory” in computer algebra is presented. Specifically, Gröbner bases are used to determine the codimension of a singularity, thereby extending the Buchberger Algorithm to modules. Also, a program in SMP is described, which permits determining whether a given function g is contact equivalent to a polynomial normal form h for one dimensional bifurcation problems up to codimension three.

Original languageEnglish (US)
Title of host publicationEUROCAL 1985 - European Conference on Computer Algebra, Proceedings
PublisherSpringer Verlag
Pages126-137
Number of pages12
ISBN (Print)9783540159841
DOIs
StatePublished - Jan 1 1985
Externally publishedYes
EventEuropean Conference on Computer Algebra, EUROCAL 1985 - Linz, Austria
Duration: Apr 1 1985Apr 3 1985

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume204 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherEuropean Conference on Computer Algebra, EUROCAL 1985
CountryAustria
CityLinz
Period4/1/854/3/85

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Armbruster, H. (1985). Bifurcation theory and computer algebra: An initial approach. In EUROCAL 1985 - European Conference on Computer Algebra, Proceedings (pp. 126-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 204 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-15984-3_245