Hopf bifurcation for maps: a frequency-domain approach

The application of the graphical Hopf theorem (GHT) as a tool for detecting invariant cycles in maps is presented. The invariant cycle emerging from the bifurcation is approximated using an analogous version of the GHT for continuous-time systems. This technique is formulated in the so-called frequency domain and it involves the use of the Nyquist stability criterion and the harmonic balance method. Some examples are included for illustration.