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

Numerische Analyse äquivarianter Evolutionsgleichungen

10-026 Joseph Paez.
Discretizing Dynamical Systems with Generalized Hopf Bifurcations

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that generalized Hopf bifurcations are shifted and turned into generalized Neimark-Sacker points by general one-step methods. We analyze the effect of discretizations methods on the emanating Hopf curve. In particular, we obtain estimates of the discretized eigenvalues along this curve. A detailed analysis of the discretized first Lyapunov coefficient is also given. The results are illustrated by a numerical example.