Summary: The Hodgkin–Huxley model was developed to characterize the action potential of a squid axon. It has served as an archetype for compartmental models of the electrophysiology of biological membranes. Thus the dynamics of the Hodgkin–Huxley model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods that can be applied to more complex models.
This note demonstrates previously unobserved dynamics in the Hodgkin–Huxley model, namely, the existence of chaotic solutions in the model with its original parameters. The solutions are found by displaying rectangles in a cross-section whose images under the return map produce a Smale horseshoe. The chaotic solutions are highly unstable, but they are significant as they lie in the basin boundary that establishes the threshold of the system.