Abstract
In the last few years, the idea that extremely interesting phenomena can be generated by adding input noise to a non-linear system has found favour with a number of research groups [1–11]. Recent studies, for example, have focused on the behaviour of bistable threshold-based systems forced by both a periodic signal with an amplitude lower than the threshold and a stochastic component. The phenomenon involves a rapid increase in the signal-to-noise ratio, with an optimal noise variance value, and the presence of a peak in the output signal spectrum, corresponding to the frequency of the forcing signal. The phenomenon has been called Stochastic Resonance (SR) [1–21].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Moss and K. Wiesenfeld “The Benefits of Background Noise” Scientific American Aug. 1995, p. 50
R. Benzi, G. Parisi, A. Sutera and A. Vulpiani “Stochastic resonance in climatic change” Tellus, 34 10 (1982)
C. Nicolis “Stochastic aspects of climatic transitions — response to a periodic forcing” Tellus 34 1 (1982)
R. Benzi, G. Parisi, A. Sutera and A. Vulpiani “A theory of stochastic resonance in climatic change” SIAM J. Appl Math 43, 565 (1983)
McNamara K. Wiesenfeld and R. Roy “Observation of Stochastic Resonance in a ring laser” Phys. Rev. Lett. 60 2626 (1988)
P. Jung and P. Hanggi “Stochastic nonlinear dynamics modulated by external periodic forces” Europhys. Lett. 8 505 (1989)
G. Matteucci “Orbital forcing in a stochastic resonance model of the late Pleistocene climatic variations” Climate Dyn. 3, 179 (1989)
L. Gammaitoni N. Marchesoni, E. Menichella-Saetta and S. Santucci “Stochastic resonance in a bistable systems” Phys. Rev. Lett. 62 349 (1988, 1989)
N. Marchesoni, E. Menichella-Saetta, M. Pochini and S. Santucci “Analog simulation of underdamped stochastic systems driven by colored noise:spectral densities”, Phys. Rev. A 37, 8, 1988.
M. I. Dykman, A.L. Velikovich, G.P. Golubev, D.G. Luchinskii and S.V. Tsuprikov “Stochastic resonance in an all-optical passive bistable system” Soviet Phys JETP Lett 53, 193 (1991)
R.N. Mantegna, B. Spagnolo “Stochastic resonance in a tunnel diode” Phys. Rev. E49 R1792 (1994)
R. Benzi, A. Sutera and A. Vulpiani “The mechanism of Stochastic Resonance” J. Phys. A: Math. Gen. 14L 453 (1981)
J.P. Eckmann and L.E. Thomas “Remarks on stochastic resonance” J. Phys. A: Math. Gen. 15 L261 (1982)
S. Fauve and F. Heslot, “Stochastic resonance in a bistable system” Phys. Lett. 97A 5 (1983)
B. McNamara and K. Wiesenfeld “Theory of Stochastic Resonance” Phys. Rev. A39 (1989)
T.L. Carrol and L.M. Pecora “Stochastic Resonance and Crises” Phys. Rev. Lett. 70 576 (1993)
M.I. Dykman, R. Mannella, P.V.E. McClintock and N.G. Stocks “Comment on Stochastic Resonance in bistable systems” Phys. Rev. Lett. 65, 2606 (1990)
L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta and S. Santucci “Reply to comment on: Stochastic Resonance in Bistable Systems” Phys. Rev. Lett. 65, 2607 (1990)
L. Gammaitoni “Stochastic resonance in multi-threshold systems” Phys. Lett. A 208 315 (1995)
Gammaitoni L. Hanggi P. Jung P. Marchesoni F. “Stochastic Resonance” Reviews of Modern Physics. 70(l):223–287, 1998 Jan.
Dykman MI. Mcclintock PVE. “What can stochastic resonance do” Nature. 391(6665):344, 1998 Jan 22.
M.F. Wadgy, “Effect of various dither forms on quantizzation errors of ideal A/D converters”, IEEE Trans. Instrum. Measu., vol.38, n.4, 1989.
L. Schuchman, “Dither signals and their effect on quantizzation noise”, IEEE Trans. Commun. Technol., vol.12, 1964.
J. Vanderkooy and S.P. Lipshitz, “Dither in digital audio”, J. Audio Eng. Soc, vol.35, n.12, 1987.
P. Carbone, D. Petri, “Effect of Additive Dither on the Resolution of Ideal Quantisers”, IEEE Trans. Instrum. Meas.; 1994, 43, 3, 389–396
Gammaitoni L., Marchesoni F., Santucci S., “Stochastic Resonanc as a Bona Fide Resonance”, Phys. Rev. 14/1, 1995, 1052.
R. M. Gray, T. G. Stockoham, Dithered Quantisers, IEEE Trans. Inf. Th..; 1993, 39, 3, 805–812
L. Gammaitoni, “Stochastic resonance and the dithering effect in threshold physical systems”, Phys. Rev. E.; 1995, 52, 5, 4691–4698
A. Papoulis, “Probability, Random Variables, and Stochastic Process”, McGRAW-HILL BOOK COMPANY.
J.M.T. Thompson and H.B. Stewart, “Nonlinear dynamics and chaos”, John Wiley and Sons, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Andò, B., Graziani, S. (2000). An Overview of Noise Added Systems. In: Andò, B., Graziani, S. (eds) Stochastic Resonance. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4391-6_2
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4391-6_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6975-2
Online ISBN: 978-1-4615-4391-6
eBook Packages: Springer Book Archive