Action potential solitons and waves in axons

Abstract

We show that the action potential signals generated by the Hodgkin–Huxley cable model are reaction–diffusion-type solitons and waves. Within the framework of the cable equation, action potential spikes generated by injected currents at the middle of the axon originate travelling spikes propagating in opposite directions of the axon. Action potential spikes travelling in opposite directions of the axon annihilate when colliding with each other or with the axon boundaries. Through numerical simulations, we characterise the properties of these action potentials, deriving their characteristic curves and speeds. In the spiking region of the HH model, different spikes have different speeds. We propose several tests to validate or falsify the Hodgkin–Huxley cable model.