Speed of spread of excitation in a reduced Hodghn-Huxley model-III. Integral differential equation

The set of Hodgkin-Huxley equations with the slow variables neglected is reduced to an integral differential equation. The limiting cases of fast and slow relaxation are examined. In the first case the problem is reduced to a non-linear differential equation for the potential and in the second to an ordinary differential equation with the function of source, thanks to the approximation of a steady sodium variable, as a step function. The accuracy of this approximation is evaluated by constructing the first approximation for the source function.