Bifurcation theory and computer algebra: An initial approach

  • D. Armbruster
Applications I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


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.


Normal Form Bifurcation Diagram Bifurcation Point Computer Algebra Existence Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • D. Armbruster
    • 1
  1. 1.Institute for Information SciencesUniversity of TübingenTübingenGermany

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