Order reprints

Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons

Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora

*Corresponding author:  

MBE2014,2,189doi:10.3934/mbe.2014.11.189

With the aim to describe the interaction between a couple of neurons a stochastic model is proposed and formalized. In such a model, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons and when a spike of the other one occurs it is turned on. The initial and after spike reset positions do not allow to identify the inter-spike intervals with the corresponding first passage times. However, we are able to apply some well-known results for the first passage time problem for the Ornstein-Uhlenbeck process in order to obtain (i) an approximation of the probability density function of the inter-spike intervals in one-way-type interaction and (ii) an approximation of the tail of the probability density function of the inter-spike intervals in the mutual interaction. Such an approximation is admissible for small instantaneous firing rates of both neurons.

Please supply your name and a valid email address you yourself

Fields marked*are required

Article URL   http://www.aimspress.com/MBE/article/2428.html
Article ID   1551-0018_2014_2_189
Editorial Email  
Your Name *
Your Email *
Quantity *

Copyright © AIMS Press All Rights Reserved