ABSTRACT
The above paragraph provides a short survey of research carried out to date in this field, for the most part on bistable dynamic systems, i.e., systems whose dynamics can be underpinned by a double-welled "potential function". However, SR is by definition a threshold process. One assumes that the deterministic periodic modulation is too weak to cause transitions over the potential barrier in the absence of the noise; then even small amounts of added white noise will lead to noise-assisted barrier crossings, thereby enhancing the output signal-to-noise-ratio of the system. This, in turn, begs the question of whether similar cooperative effects can be seen in the response of a simpler system, quantified solely in tenns of threshold crossing events. The fact that SR may indeed be a feature of signal processing by sensory neurons and that there exist simpler mathematical models of neural firing than the bistable models referred to above, provides further momentum to this question. A very recent paper by Wiesenfeld et. al. [16] describes SR in the response of a simple system, one in which a state point makes an excursion to a barrier, under the influence of white noise and a weak periodic signal; after surmounting the barrier (which is impossible without the noise) the state point is returned deterministically to its starting point. This system can be used as a prototype of a variety of
"excitable systems", some of which are known to provide very good descriptions of certain properties of excitable cells. Indeed, Wiesenfeld et. al. are able to match the predictions of their generic theory quite well with analog simulations of a Fitzhugh-Nagummo model of the neuron, as well as experimental data from the mechano-receptor of the Missouri crayfish stimulated by external noise and a weak periodic modulation. The predictions match the simulations even though, unlike other single-state treatments of SR [17], they do not explicitly consider a system dynamics described by a monostable potential.
