title: [Rate of excitation propagation in a reduced Hodgkins-Huxley model. III. Integrodifferential equations].
abstract: The Hodgkin - Huxley system of equations is reduced to single integral-differential equation in neglection of slow variables dynamics. Two limiting cases of fast and slow sodium activation processes are considered. The first case leads to a nonlinear differential equation for the potential, the second one - to an ordinary differential equation with a known source as a function of coordinate. Such a simplification is due to approximation of steady-state sodium activation variable with the help of Heviside function. The validity of this approximation is discussed; the corresponding error is estimated by calculation of the second approximation for the source function.
mesh_terms: D008433:Mathematics; D008959:Models, Neurological; D009431:Neural Conduction
vernacular_title: O skorosti rasprostraneniia vozbuzhdeniia v redutsirovannoĭ modeli  Khodzhkina--Khaksli. III. Integrodifferentsial'noe uravenie