A special point of Z2-codimension three Hopf bifurcation in the Hodgkin-Huxley model Original Research Article

A curve in (I,T,gNa,vNa)-parameter space of degenerate Hopf bifurcation for the Hodgkin-Huxley model is described. The curve includes all six of the “doubly degenerate” points from our earlier work [1,2]. The curve includes one special point at which m = 1, where m is the modal parameter. The recognition problem for the singularity at this point is solved. Assuming that the parameters (T,gNa,vNa) provide a versal unfolding, all previously known types of Hopf bifurcation behavior in the Hodgkin-Huxley system will be exhibited for (T,gNa,vNa) in a neighborhood of their values at this point.