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; wherein switching the electronic synaptic device to an OFF state or to a multilevel ON state occurs by applying a pre-synaptic voltage pulse and a post-synaptic voltage pulse to the first and second electrodes, respectively, wherein the post-synaptic voltage pulse has an opposite polarity to the pre-synaptic voltage pulse, wherein magnitude of the pre-synaptic voltage pulse and the post-synaptic voltage pulse each are below a switching voltage magnitude threshold, and a difference in magnitude between the pre-synaptic voltage pulse and the post-synaptic voltage pulse exceeds the switching voltage magnitude threshold by an amount, wherein the amount is a function of a relative timing between the pre-synaptic voltage pulse and the post-synaptic voltage pulse, and conductance of the composite medium is controlled by the relative timing between the pre-synaptic voltage pulse and the post-synaptic voltage pulse, and wherein the composite medium material determines whether the pre-synaptic voltage pulse, the post-synaptic voltage pulse and delay between the pre-synaptic voltage pulse and the post-synaptic voltage pulse combine to form a setting voltage less than the switching voltage magnitude threshold.