Eur. Phys. J. B 72, 279-287 (2009)
https://doi.org/10.1140/epjb/e2009-00309-x

Output stream of binding neuron with delayed feedback

Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14-B, 03680 Kyiv, Ukraine

Corresponding author: ^a vidybida@bitp.kiev.ua

Received: 29 January 2009
Revised: 23 July 2009
Published online: 17 September 2009

Abstract

A binding neuron (BN) with delayed feedback is considered. The neuron is fed externally with a Poisson stream of intensity λ. The neuron's output spikes are fed back into its input with time delay Δ. The resulting output stream of the BN is not Poissonian. The main purpose of this paper is to find interspike intervals (ISI) distribution of the output stream. For BN with threshold 2 the exact mathematical expressions as functions of λ, Δ and BN's internal memory, τ are derived for the ISI distribution and coefficient of variation. For higher thresholds these quantities are found numerically. The distributions found are characterized with jumps, derivative discontinuities and include singularity of Dirac's δ-function type. The ISI coefficient of variation found is a unimodal function of input intensity, with the maximum value considerably bigger than unity. It is concluded that delayed feedback presence can radically alter neuronal output firing statistics.