Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

09-056 Joseph Paez.
Discretizing Bifurcation Diagrams near Codimension two Singularities

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that fold-Hopf singularities are O(hp)-shifted and turned into fold-Neimark-Sacker points by one-step methods of order p. Then we analyze the effect of discretizations methods on the local bifurcation diagram near Bogdanov- Takens and fold-Hopf singularities. In particular we prove that the discretized codimension one curves intersect at the singularities in a generic manner. The results are illustrated by a numerical example.