The statistical dynamics of an impulse induced quanta turnover is studied by means of a nonstationary stochastic model--double barrier synapse--resulting from a previously developed mathematical theory of chemical synaptic transmission. An essential aspect of nonstationarities of the model is that the interpool quanta transfers follow binomial distribution at impulse arrival time, while in the absence of stimulation they obey Yule-Furry statistics. Under a variety of conditions, corresponding to those in actual experiments, the transient behaviour of the model is simulated and analysed in detail. As a result, the quantitative description of immediate and delayed components of synaptic action is introduced. If simulations of quantal fluctuations are performed numerically, then for the treatment of dynamic regularities, besides numerical procedures, an analytical method of envelopes is developed. It is supported by the theorems which reduce behaviour of the double-barrier synapse to the super-position of simpler solutions for single-barrier systems. With short-term facilitation quantitative analysis and simulations, the synaptic resonance phenomenon is theoretically predicted: different resonant frequencies are found at different levels of facilitation. The importance of this phenomenon treated as a clue to the information processing capabilities of a chemical synapse is discussed.