1.5. STOCHASTIC RESONANCE IN MODELS FROM ELECTRONICS TO BIOLOGY 23 Figure 1.14. The input-output characteristic (hysteresis loop) of the Schmitt trigger. and period T 0, for example, to V+, we periodically modulate the critical level. After adding a random noise at the input, the system is able to jump between the two states ±V . As in the example of glacial cycles we can consider a discontinuous modulation, for instance given by V+(t) = a sign(sin ( 2πt T )). The whole picture is now similar to the one in (1.3). Here the periodic modulation of the reference voltage corresponds to the tilting of the potential wells. Fauve and Heslot [38] studied the power spectrum of the system and, as in the glacial cycle example, established that the energy carried by the spectral component of Y at a given driving frequency has a local maximum for a certain intensity of the input noise. The Schmitt trigger provides another interpretation to the phenomenon of sto- chastic resonance. A system displaying stochastic resonance can be considered as a random amplifier. The weak periodic signal which cannot be detected in the absence of noise, can be successfully recovered if the system (the Schmitt trigger or (1.3)) is appropriately tuned. In other words, the weak underlying periodicity is exhibited at appropriately chosen non-zero levels of noise, and gets lost if noise is either too small or too large. To date, the most important application area of threshold models is neural dynamics (see Bulsara et al. [17], Douglass et al. [29], Patel and Kosko [85]) and transmission of information (see Neiman et al. [81], Simonotto et al. [99], Stocks [101], Moss et al. [79]). The recent book [73] by McDonnell et al. gives a very complete account on the theory of non-dynamic or threshold stochastic resonance. 1.5.3. The paddlefish. In this well known and frequently discussed example stochastic resonance appears in the noise-enhanced feeding behavior of the pad- dlefish Polyodon spathula (see Greenwood et al. [47], Russel et al. [95], Freund et al. [42]). This species of fish lives in the Midwest of the United States and in the Yangtze River in China, and feeds on the zooplankton Daphnia. To detect its prey animals under limited visibility conditions at river bottoms, the paddlefish uses the long rostrum in front of its mouth as an electrosensory antenna. The frequency range of sensitivity of the rostrum’s electroreceptors well overlaps with the range of frequencies produced by the prey. Roughly, the capture probability is observed as a function of the position of the prey relative to the rostrum. In experiments, external noise was generated by electrodes connected to an electric noise genera- tor. It was observed that the spatial distribution and number of strike locations
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