Distribution of interspike intervals of a neuron with inhibitory autapse stimulated with a renewal process

TL;DR

This paper analytically derives the exact distribution of interspike intervals for neurons with inhibitory autapses stimulated by renewal processes, revealing how feedback influences neuronal firing patterns.

Contribution

It provides a model-independent analytical expression for the ISI distribution in neurons with inhibitory feedback, applicable to various neuron models and input distributions.

Findings

Exact ISI distribution derived without approximations

Explicit initial ISI PDF for Erlang-2 input distribution

Application to threshold-2 neuronal models

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 non-adaptive 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 Erlang-2 distribution. In that case we have found explicitly the model-independent initial part of ISIs PDF $p(t)$ defined at some initial interval $[0;T_2]$ of ISI values.