A diffusion equation for the transition p.d.f. describing the time evolution of the membrane potential for a model neuron, subjected to a Poisson input, is obtained, without breaking up the continuity of the underlying random function. The transition p.d.f. is calculated in a closed form and the average firing interval is determined by using the steady-state limiting expression of the transition p.d.f. The Laplace transform of the first passage time p.d.f. is then obtained in terms of Parabolic Cylinder Functions as solution of a Weber equation, satisfying suitable boundary conditions. A continuous input model is finally investigated.
Diffusion approximation and first passage time problem for a model neuron / R. M., Capocelli; Ricciardi, LUIGI MARIA. - In: KYBERNETIK. - ISSN 0023-5946. - STAMPA. - 8:6(1971), pp. 214-223. [10.1007/BF00288750]
Diffusion approximation and first passage time problem for a model neuron
RICCIARDI, LUIGI MARIA
1971
Abstract
A diffusion equation for the transition p.d.f. describing the time evolution of the membrane potential for a model neuron, subjected to a Poisson input, is obtained, without breaking up the continuity of the underlying random function. The transition p.d.f. is calculated in a closed form and the average firing interval is determined by using the steady-state limiting expression of the transition p.d.f. The Laplace transform of the first passage time p.d.f. is then obtained in terms of Parabolic Cylinder Functions as solution of a Weber equation, satisfying suitable boundary conditions. A continuous input model is finally investigated.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.