Discretizing dynamical systems with Hopf–Hopf bifurcations

We study the discretization of two-parameter, continuous-time dynamical systems. We prove that one-step methods turn Hopf–Hopf bifurcations into double Neimark–Sacker points. We discuss the effect of the discretization methods on the bifurcation diagram. The numerical approximation of the critical eigenvalues is analysed. The results are illustrated by a numerical example.