Symbolic Equilibrium Point Analysis in Parameterized Polynomial Fields

V. G. Ganzha, E. W. Mayr und E. V. Vorozhtsov (Editoren)
M. El Kahoui und Andreas Weber
In proceedings of Computer Algebra in Scientific Computing (CASC~2002), pages 71-83, Sept. 2002
 

Abstract

It is well known that various questions of stability of polynomial vectors fields can be reduced to quantifier elimination problems on real closed fields. More recently we have shown that also the parametric question of the occurence of Hopf bifurcations can be decided by quantifier elimination. The combination of general purpose quantifier elimination systems has been sufficient to solve some of the occuring quantifier elimination problems but did not succeed for many others (on current computers). For the common case of equilibrium points with nonzero Jacobian determinant we will show that there is a computationally well suited description that can serve as an infrastructure for more efficient methods.

Bibtex

@INPROCEEDINGS{ElKahouiWeber 2002a,
     author = {El Kahoui, M. and Weber, Andreas},
     editor = {Ganzha, V. G. and Mayr, E. W. and Vorozhtsov, E. V.},
      pages = {71--83},
      title = {Symbolic Equilibrium Point Analysis in Parameterized Polynomial Fields},
  booktitle = {Computer Algebra in Scientific Computing (CASC~2002)},
       year = {2002},
      month = sep,
   abstract = {It is well known that various questions of stability of polynomial vectors fields can be reduced to
               quantifier elimination problems on real closed fields. More recently we have shown that also the
               parametric question of the occurence of Hopf bifurcations can be decided by quantifier elimination.
               The combination of general purpose quantifier elimination systems has been sufficient to solve some
               of the occuring quantifier elimination problems but did not succeed for many others (on current
               computers). For the common case of equilibrium points with nonzero Jacobian determinant we will show
               that there is a computationally well suited description that can serve as an infrastructure for more
               efficient methods.},
       isbn = {3-9808546-0-4}
}