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.
