Mark D. McDonnell

Stochastic resonance (SR) - a counter-intuitive phenomenon in which the signal due to a weak periodic force in a nonlinear system can be {\it enhanced} by the addition of external noise - is reviewed. A theoretical approach based on linear response theory (LRT) is described. It is pointed out that, although the LRT theory of SR is by definition restricted to the small signal limit, it possesses substantial advantages in terms of simplicity, generality and predictive power. The application of LRT to overdamped motion in a bistable potential, the most commonly studied form of SR, is outlined. Two new forms of SR, predicted on the basis of LRT and subsequently observed in analogue electronic experiments, are described.

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations--e.g., random noise--cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being "suboptimal". Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the "neural code". Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise--via stochastic resonance or otherwise--than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing "noise benefits", and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

Stochastic resonance has been observed in many forms of systems, and has been hotly debated by scientists for over 30 years. Applications incorporating aspects of stochastic resonance may yet prove revolutionary in fields such as distributed sensor networks, nano-electronics, and biomedical prosthetics. Ideal for researchers in fields ranging from computational neuroscience through to electronic engineering, this book addresses in detail various theoretical aspects of stochastic quantization, in the context of the suprathreshold stochastic resonance effect. Initial chapters review stochastic resonance and outline some of the controversies and debates that have surrounded it. The book then discusses suprathreshold stochastic resonance, and its extension to more general models of stochastic signal quantization. Finally, it considers various constraints and tradeoffs in the performance of stochastic quantizers, before culminating with a chapter in the application of suprathreshold stochastic resonance to the design of cochlear implants.