Output Stream of Binding Neuron with Feedback

Abstract

The binding neuron (BN) output firing statistics is considered. The neuron is driven externally by the Poisson stream of intensity <img src="http://www.igi-global.com/Images/Symbols/m01.gif" />. The influence of the feedback, which conveys every output impulse to the input with time delay <img src="http://www.igi-global.com/Images/Symbols/m02.gif" />, on the statistics of BN's output spikes is considered. The resulting output stream is not Poissonian, and we look for its interspike intervals (ISI) distribution for the case of BN, BN with instantaneous, <img src="http://www.igi-global.com/Images/Symbols/m03.gif" />, and delayed, <img src="http://www.igi-global.com/Images/Symbols/m04.gif" />, feedback. For the BN with threshold 2 an exact mathematical expressions as functions of <img src="http://www.igi-global.com/Images/Symbols/m05.gif" />, <img src="http://www.igi-global.com/Images/Symbols/m06.gif" /> and BN's internal memory, <img src="http://www.igi-global.com/Images/Symbols/m07.gif" /> are derived for the ISI distribution, output intensity and ISI coefficient of variation. For higher thresholds these quantities are found numerically. The distributions found for the case of instantaneous feedback include jumps and derivative discontinuities and differ essentially from those obtained for BN without feedback. Statistics of a neuron with delayed feedback has remarkable peculiarities as compared to the case of <img src="http://www.igi-global.com/Images/Symbols/m08.gif" />. ISI distributions, found for delayed feedback, are characterized with jumps, derivative discontinuities and include singularity of Dirac's <img src="http://www.igi-global.com/Images/Symbols/m09.gif" />-function type. The obtained ISI coefficient of variation 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.