1. An electronic synaptic device, comprising: a first electrode; a second electrode; and a composite medium disposed between, and in contact with, the first and second electrodes, wherein the composite medium comprises a layer of discrete charge trapping particles so that an electrical resistance measured across the first and second electrodes is selectively variable; such that switching the electronic synaptic device to a binary ON state or OFF state occurs by applying opposite signed first and second voltage pulses to the first and second electrodes where magnitude of the first voltage pulse and the second voltage pulse each are below a switching voltage magnitude threshold, and a difference in magnitude between the first voltage pulse and the second voltage pulse exceeds the switching voltage magnitude threshold by an amount, wherein the amount is a function of a relative timing between the first voltage pulse and the second voltage pulse.