Bypassing Fast Time Scales of the Hodgkin-Huxley Neuron Model via a Thresholded Hard Reset

We propose a modification to the Hodgkin-Huxley model to reduce the numerical stiffness of the equations by introducing an explicit voltage threshold. When this threshold is crossed, the voltage and the gating variables are reset to constant values. It is found that, for all of the current stimuli considered, the proposed model accurately reproduces the behavior of the baseline Hodgkin-Huxley model while bypassing the fast dynamics of spiking. Specifically, the model accurately reproduces the spike times and, between spikes, the time courses of the membrane potential and gating variables.