Solutions to Hodgkin-Huxley Equations: Functional Analysis of a Molluscan Neurone

A popular way of answering the question “What functions do neurones compute?” is to construct detailed differential models and then examine their properties by numerical simulation. This approach has its limitations, many of which could be overcome if analytic solutions to the Hodgkin-Huxley [1] equations could be obtained. This paper illustrates that approximate solutions to these equations do exist. These solutions are in the form of Volterra functional expansions of the state equations of the differential model.