Preprint of the project:
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.
