  Artificial neural networks (ANNs) have been extensively used for the
description of problems arising from biological systems and for constructing
neuromorphic computing models. The third generation of ANNs, namely, spiking
neural networks (SNNs), inspired by biological neurons enable a more realistic
mimicry of the human brain. A large class of the problems from these domains is
characterized by the necessity to deal with the combination of neurons, spikes
and synapses via integrate-and-fire neuron models. Motivated by important
applications of the integrate-and-fire of neurons in neuromorphic computing for
bio-medical studies, the main focus of the present work is on the analysis of
the effects of additive and multiplicative types of random input currents
together with a random refractory period on a leaky integrate-and-fire (LIF)
synaptic conductance neuron model. Our analysis is carried out via Langevin
stochastic dynamics in a numerical setting describing a cell membrane
potential. We provide the details of the model, as well as representative
numerical examples, and discuss the effects of noise on the time evolution of
the membrane potential as well as the spiking activities of neurons in the LIF
synaptic conductance model scrutinized here. Furthermore, our numerical results
demonstrate that the presence of a random refractory period in the LIF synaptic
conductance system may substantially influence an increased irregularity of
spike trains of the output neuron.
