Two-parameter bifurcation in a two-dimensional simplified Hodgkin–Huxley model

The dynamical behaviors of a two-dimensional simplified Hodgkin–Huxley model exposed to external electric fields are investigated based on the qualitative analysis and numerical simulation. A necessary and sufficient condition is given for the existence of the Hopf bifurcation. The stability of equilibrium points and limit cycles is also studied. Moreover, the canards and bifurcation are discussed in the simplified model and original model. The dynamical behaviors of the simplified model are consistent with the original model. It would be a great help to further investigations of the original model.

► A two-dimensional simplified Hodgkin–Huxley model with two parameters is shown.
► The necessary and sufficient condition is given for the existence of the Hopf bifurcation.
► The stability of equilibrium points and limit cycles are also investigated.
► The canards and bifurcation are discussed in the simplified model and original model.