Effects of random jumps on a very simple neuronal diffusion model

The effects of taking into account in a perfect integrate and fire model of neuronal activity the spatial localization of the synapses are studied by superposing to the diffusion a simple discrete jump component. Different criteria are employed to assess the role of excitatory and inhibitory discrete contributions. Comparisons are performed with respect to the case where contributions coming from synapses more distal from the trigger zone are summed up in a continuous model. A systematic study of the output frequency and of the inter spike interval coefficient of variation (CV) is performed by means of examples as the model parameters are varied.