Firing statistics of a neuron with delayed feedback inhibition stimulated with a renewal process
Year: 2021
Type: preprint
Abstract: In this paper, we study the impact of an inhibitory autapse on neuronal activity. In order to do this, we consider a class of spiking neuron models with delayed feedback inhibition stimulated with a series of excitatory impulses, representing a stochastic point renewal process. We calculate exactly the probability density function (PDF) $p(t)$ for the distribution of output interspike intervals (ISIs). The calculation is based on the known PDF of ISIs $p^0(t)$ for the same neuron without feedback and the PDF of ISIs for the input stream $p^{in}(t)$. Obtained results are applied to the case of a neuron with threshold 2 when the time intervals between input impulses are distributed according to the Erlang-2 distribution. Further, for the binding neuron model with threshold 2 with delayed feedback inhibition stimulated with the Erlang-2 stream of excitatory impulses, the first two moments of the ISI PDF are computed. Our results indicate that depending on the time delay of the feedback inhibition, the spike regularity can lower or rise in comparison with the case of the neuron without delayed feedback inhibition.
Source: arXiv (Cornell University)
Authors: Olha Shchur, A. K. Vidybida
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3206903866