A neuron model with pre-synaptic deletion and post-synaptic accumulation decay, and threshold behaviour

Abstract

A stochastic model is proposed for a neuron which has an inhibitory stream interacting pre-synaptically with an excitatory stream. Uninhibited excitatories have a post-synaptic effect of increasing the membrane potential by random amounts, with the potential decaying linearly to zero in the absence of inputs. When the potential reaches a threshold level, the neuron fires. The Laplace transform of the probability density function of the interval between two successive firings is derived. The mean and the variance are obtained for exponential inter-arrival times and inputs as an example.