Bifurcations Features of the Hodgkin-Huxley Neuron Model

The features of bifurcations at threshold activation of the Hodgkin-Huxley neuron model are considered in the paper. It is shown that at different shape and parameters of threshold activation signals for the Hodgkin-Huxley neuron model after setting to zero value of the input current pulse of activation the shape of the time behavior of the four state variables of the neuron model are almost the same for different shapes of the input pulse. This makes it possible to obtain the set of bifurcation values of the Hodgkin-Huxley model parameters after appropriate scaling. These results can be used for solving the problem of determining the energy optimal activation pulse.