Stochastic resonance: the role of potential asymmetry and non Gaussian noises

Abstract

Within the two state theory TST for stochastic resonance SR we analize two di erent aspects: a the extension of the TST in order to include potential asymmetry i.e.: the states show di erent stabilities; b the evaluation of transition rates for systems whose stationary distribution is non Gaussian. We apply the results of a to study the role of the potential symmetry for SR in bistable systems, observing that the signal-to-noise ratio increases with the symmetry of the potential of the system indicating that it is this feature that governs the optimization of the response. We apply the results of b to discuss SR in situations where we can assume that the noise is non Gaussian, and discuss its relation with experimental results in sensory systems. I IntroductionThe phenomenon of stochastic resonance SR has attracted considerable interest in the last decade due, among other aspects, to its potential technological applications for optimizing the output signal-to-noise ratio SNR in nonlinear dynamical systems as well as its relation with some biological mechanisms. The phenomenon shows the counterintuitive role played by noise in nonlinear systems as it contributes to enhance the response of a system subject to a weak external signal. There is a wealth of papers, conference proceedings and reviews on this subject 1 , Ref. 2 being the most recent one, showing the large number of applications in science and technology, ranging from paleoclimatology 3 , to electronic circuits 4 , lasers 5 , chemical systems 6 , and the connection with some situations of biological interest noise-induced information ow i n sensory neurons in living systems, the in uence in ionchannel gating or in visual perception 7 . A tendency shown in recent papers, and determined by the possible technological applications, points towards achieving an enhancement of the system response that is: obtaining a larger output SNR by means of the coupling of several SR units in what conforms an extended m e dium 8, 9, 10 .A v ast majority of studies on SR have been done analyzing a paradigmatic system: a bistable onedimensional double-well system. Among the bistable models there is one that singles out: the two-state model TST 3, 11 . Such a model has proven to be extremely useful for the understanding of the SR phenomenon, offering also a simple framework to provide analytical results. Most of the studies have been carried out in the symmetric case. However, even in the earliest account of the TST 3 the possibility of asymmetry was introduced with the conclusion that the symmetric case would be the optimal one. Other authors have also partially analyzed this case see references in 2 for instance considering equal curvatures of the potential wells 12 . A more recent and related work 13 lacks a detailed analysis of the role of the symmetry while other points requiere to be clari ed.In almost all descriptions, and particularly within the TST, the transition rates between the two w ells are estimated as the inverse of the mean rst-passage-time. Such a passage ...

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