Preprint of the project:
10-024 Joseph Paez.
Discretizing Dynamical Systems with Hopf-Hopf Bifurcations
We consider parameter-dependent,
continuous-time dynamical systems under discretizations. It is shown
that Hopf-Hopf bifurcations are O(hp)-shifted and turned into double
Neimark-Sacker points by general one-step methods of order p. Then we
discuss the effect of discretization methods on the emanating Hopf
curves. The numerical approximation of the critical eigenvalues is
analyzed too. The results are illustrated by a numerical
example.
