Spontaneous Oscillations in Hodgkin-Huxley Model

Automatic neuron firing is an important and interesting research subject in neuroelectrophysiology. Through the original Hodgkin-Huxley model, we investigate its codimension 1 bifurcations along maximum conductance of the sodium channel, maximum conductance of potassium channel, and extracellular potassium concentration. We find that increasing maximum conductance of sodium channel, or decreasing maximum conductance of potassium channel, or increasing extracellular potassium concentration will all cause spontaneous oscillation without any external stimulus current. The effect of increasing extracellular potassium concentration will cause repetitive neuron firing has been verified by experiments, but the effect that changing maximum channel conductance will cause automatic neuron firing is first analyzed in the current paper but not yet verified by experiments. We hope the experiment can be done in the future by using sodium channel activator and potassium channel blocker.