1.5. STOCHASTIC RESONANCE IN MODELS FROM ELECTRONICS TO BIOLOGY 25 modulations and random noise were imposed on the environment. The firings pro- duced by the mechanoreceptor cell were recorded for different noise levels, and show clear stochastic resonance peaks as functions of noise intensity. Similar phenomena are encountered on a much more general basis in the exchange of substances or information through ionic channels on cell membranes in living organisms. 1.5.5. Physiological systems. The fact that sensory neurons are excitable systems leading to the FitzHugh–Nagumo equations in the preceding subsection, is also basic for many suggestions of how to make use of the phenomenon of stochastic resonance in medicine. Disfunctions arising in sensory organs responsible for hear- ing, tactile or visual sensations or for balance control could result from relatively higher sensitivity thresholds compared with those of healthy organs. To raise the sensitivity level, a natural idea seems to be to apply the right amount of external noise to these dysfunctional organs, in order to let stochastic resonance effects am- plify weak signal responses. In experiments reported in Collins et al. [21], local indentations were applied to the tips of digits of test persons who had to correctly identify whether a stimulus was presented. Stimuli generated by subthreshold sig- nals garnished with noise led to improvements in correct identification, with some optimal noise level indicating a stochastic resonance point. Results like this may be used for designing practical devices, as for instance gloves, for individuals with ele- vated cutaneous sensory thresholds. Similarly, randomly vibrating shoe inserts may help restoring balance control (see Priplata et al. [89]). Stochastic resonance effects may be used for treating disfunctions of the human blood pressure system (barore- flex system) featuring a negative feedback between blood pressure and heart rate resp. width of blood vessels. Blood pressure is monitored by two types of receptors, for arteries and veins. In Hidaka [54], a weak periodic input was introduced at the venous blood pressure receptor, whereas noise was added to the arterial receptor. It was shown that the power of the output signal of the heart rate (measured by an electrocardiogram) as a function of noise intensity exhibits a bell-shape form, typical for a curve with a stochastic resonance point. Another group of possible medical applications of the amplification effects of stochastic resonance is related to the human brains information processing activity (see Mori and Kai [78]). In an experiment in Usher and Feingold [103] the effect of stochastic resonance in the speed of memory retrieval was exhibited. Test persons were proven to perform single digit calculations (e.g. 7 × 8 =?) significantly faster when exposed to an optimal level of acoustic noise (via headphones). 1.5.6. Optical systems. In optical systems, stochastic resonance was first observed in McNamara et al. [75] and Vemuri and Roy [104] in a bidirectional ring laser, i.e. a ring resonator with a dye as lasing medium. This laser system supports two meta-stable states realized as modes of the same frequency that travel in oppo- site directions. They are strongly coupled to each other by the lasing medium, thus permitting a bistable operation. When the pumping exceeds the lasing threshold, either clockwise or counterclockwise modes propagate in the laser, with switchings between those two modes initiated by spontaneous emission in the active medium, and fluctuations of the pump laser. The net gains of the two propagating modes in opposite directions can be controlled by an acousto-optical modulator inside the cavity, which thus can be used both to impose a periodic switching rate between the modes and to inject noise. Therefore the resulting semiclassical laser equations
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