Abstract
A model of activities of a single neuron is presented. It has a large number of input lines and is composed of three main parts : an adder, a filter and a threshold element. Under some reasonable assumptions, the output of the filter can be treated as a random process, and the first passage times (FPTs) for this process correspond to the intervals of successive output pulses from the model.
Two kinds of random processes are examined. The first is known as the Erlang's system in telephone traffic theory. The mathematical expression of the probability density function (pdf) of the FPTs is obtained for this process. The second process is resulted from the filtering of the input random pulse train by a single stage RC filter. The FPTs are obtained by the digital computer simulation.
The main results obtained are as follows:
1) The output pulses form a renewal process, and the output process is completely characterized by the distribution of pulse intervals.
2) The pdf of output pulse intervals is expressed as the sum of several terms of exponential functions.
3) When the input pulse density increases, the pdf tends to that of a Gamma distribution.
4) When the input pulse density decreases, the pdf tends to that of an exponential distribution.
5) The mean pulse density input-output characteristics of the model are nearly linear when the threshold is low, and become highly nonlinear when the threshold grows higher.
