Affordable Access

Publisher Website

Deciding Hopf Bifurcations by Quantifier Elimination in a Software-component Architecture

Authors
Journal
Journal of Symbolic Computation
0747-7171
Publisher
Elsevier
Publication Date
Volume
30
Issue
2
Identifiers
DOI: 10.1006/jsco.1999.0353
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract In this paper we give a semi-algebraic description of Hopf bifurcation fixed points for a given parameterized polynomial vector field. The description is carried out by use of the Hurwitz determinants, and produces a first-order formula which is transformed into a quantifier-free formula by the use of usual-quantifier elimination algorithms. We apply techniques from the theory of sub-resultant sequences and of Gröbner bases to come up with efficient reductions, which lead to quantifier elimination questions that can often be handled by existing quantifier elimination packages. We could implement the algorithms for the conditions on Hopf bifurcations by combining the computer algebra system Maple with packages for quantifier elimination using a Java-based component architecture recently developed by the second author. In addition to some textbook examples we applied our software system to an example discussed in a recent research paper.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Hopf bifurcations via zero sets

on Journal of Computational and A... Jan 01, 1994

On the analysis of hopf bifurcations

on International Journal of Engin... Jan 01, 1983

Hopf bifurcations in resonance 2:1

on Nonlinear Analysis Theory Meth... Jan 01, 2003
More articles like this..