Spiking Activity of a LIF Neuron in Distributed Delay Framework

Abstract

Evolution of membrane potential and spiking activity for a single leaky integrate-and-fire (LIF) neuron in distributed delay framework (DDF) is investigated. DDF provides a mechanism to incorporate memory element in terms of delay (kernel) function into a single neuron models. This investigation includes LIF neuron model with two different kinds of delay kernel functions, namely, gamma distributed delay kernel function and hypo-exponential distributed delay kernel function. Evolution of membrane potential for considered models is studied in terms of stationary state probability distribution (SPD). Stationary state probability distribution of membrane potential (SPDV) for considered neuron models are found asymptotically similar which is Gaussian distributed. In order to investigate the effect of membrane potential delay, rate code scheme for neuronal information processing is applied. Firing rate and Fano-factor for considered neuron models are calculated and standard LIF model is used for comparative study. It is noticed that distributed delay increases the spiking activity of a neuron. Increase in spiking activity of neuron in DDF is larger for hypo-exponential distributed delay function than gamma distributed delay function. Moreover, in case of hypo-exponential delay function, a LIF neuron generates spikes with Fano-factor less than 1.