Distribution of interspike intervals of a neuron with inhibitory autapse stimulated with a renewal process
Abstract
In this paper, we study analytically the impact of an inhibitory autapse on neuronal activity. In order to do this, we formulate conditions on a set of nonadaptive spiking neuron models with delayed feedback inhibition, instead of considering a particular neuronal model. The neuron is stimulated with a stochastic point renewal process of excitatory impulses. Probability density function (PDF) $p(t)$ of output interspike intervals (ISIs) of such a neuron is found exactly without any approximations made. It is expressed in terms of ISIs PDF for the input renewal stream and ISIs PDF for that same neuron without any feedback. Obtained results are applied to a subset of neuronal models with threshold 2 when the time intervals between input impulses are distributed according to the Erlang2 distribution. In that case we have found explicitly the modelindependent initial part of ISIs PDF $p(t)$ defined at some initial interval $[0;T_2]$ of ISI values.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 DOI:
 10.48550/arXiv.2110.11161
 arXiv:
 arXiv:2110.11161
 Bibcode:
 2021arXiv211011161S
 Keywords:

 Quantitative Biology  Neurons and Cognition;
 Physics  Biological Physics
 EPrint:
 12 pages, 3 figures