  Activity of inhibitory neuron with delayed feedback is considered in the
framework of point stochastic processes. The neuron receives excitatory input
impulses from a Poisson stream, and inhibitory impulses from the feedback line
with a delay. We investigate here, how does the presence of inhibitory feedback
affect the output firing statistics. Using binding neuron (BN) as a model, we
derive analytically the exact expressions for the output interspike intervals
(ISI) probability density, mean output ISI and coefficient of variation as
functions of model's parameters for the case of threshold 2. Using the leaky
integrate-and-fire (LIF) model, as well as the BN model with higher thresholds,
these statistical quantities are found numerically. In contrast to the
previously studied situation of no feedback, the ISI probability densities
found here both for BN and LIF neuron become bimodal and have discontinuity of
jump type. Nevertheless, the presence of inhibitory delayed feedback was not
found to affect substantially the output ISI coefficient of variation. The ISI
coefficient of variation found ranges between 0.5 and 1. It is concluded that
introduction of delayed inhibitory feedback can radically change neuronal
output firing statistics. This statistics is as well distinct from what was
found previously (Vidybida & Kravchuk, 2009) by a similar method for excitatory
neuron with delayed feedback.
