We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such "single-trigger" systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neutrons in the crayfish.
Stochastic resonance is by now a well studied phenomenon whereby certain nonlinear systems, subject to weak input signals, have the property that the presentation of stochastic forcing, or “noise,” can enhance the coherence of the output. Since its introduction in 1981, this curious phenomenon has been the object of much study, yet a number of questions remain. In addition to offering an update to recent reviews, we hope here to set the stage with a brief tutorial, raise some questions and then to offer a speculative look towards the future.
Recently, biological preparations which are thought to be chaotic have been controlled using algorithms based on the detection and manipulation of periodic unstable points. The dynamics of these systems are, however, contaminated with noise; thus detection becomes a statistical process. Here we show that low dimensional chaos can be reliably detected with large noise contamination and distinguished from noisy limit cycles. We also examine a purely chaotic high dimensional system.
Many neurons at the sensory periphery receive periodic input, and their activity exhibits entrainment to this input in the form of a preferred phase for firing. This article describes a modeling study of neurons which skip a random number of cycles of the stimulus between firings over a large range of input intensities. This behavior was investigated using analog and digital simulations of the motion of a particle in a double-well with noise and sinusoidal forcing. Well residence-time distributions were found to exhibit the main features of the interspike interval histograms (ISIH) measured on real sensory neurons. The conditions under which it is useful to view neurons as simple bistable systems subject to noise are examined by identifying the features of the data which are expected to arise for such systems. This approach is complementary to previous studies of such data based, e.g., on non-homogeneous point processes. Apart from looking at models which form the backbone of excitable models, our work allows us to speculate on the role that stochastic resonance, which can arise in this context, may play in the transmission of sensory information.
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