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In this paper we present a simple microscopic stochastic model describingshort term plasticity within a large homogeneous network of interactingneurons. Each neuron is represented by its membrane potential and by theresidual calcium concentration within the cell at a given time. Neurons spikeat a rate depending on their membrane potential. When spiking, the residualcalcium concentration of the spiking neuron increases by one unit. Moreover, anadditional amount of potential is given to all other neurons in the system.This amount depends linearly on the current residual calcium concentrationwithin the cell of the spiking neuron. In between successive spikes, thepotentials and the residual calcium concentrations of each neuron decrease at aconstant rate.  We show that in this framework, short time memory can be described as thetendency of the system to keep track of an initial stimulus by staying within acertain region of the space of configurations during a short but macroscopicamount of time before finally being kicked out of this region and relaxing toequilibrium. The main technical tool is a rigorous justification of the passageto a large population limit system and a thorough study of the limit equation.

A system of interacting neurons with short term synaptic facilitation