Numerical computation of degenerate Hopf bifurcation points

In this paper a numerical method for the detection and computation of degen erate Hopf bifurcation points is presented. The degeneracies are classified and defining equations characterizing each of the equivalence classes are constructed by means of a generalized Liapunov-Schmidt reduction. The numer ical computation of the sign of the first Liapunov coefficient which determ ines the stability of the bifurcating periodic orbits is discussed as well. Numerical experiments are performed for the clamped Hodgkin-Huxley equatio ns.