Discretizing the Hopf–Hopf bifurcation

Abstract

In this presentation we study the one-step discretization of ODEs with a Hopf–Hopf Bifurcation. We analyze how the local bifurcation diagram  is  perturbed  by  the  one-step  methods.  The  numerical  approximation  of  the  critical  eigenvalues is  also  discussed.  We  interpret  the obtained results in terms of perturbation of branching points. We illustrate the main results by means of numerical experiments.