Abstract
There are well-known and strictly regulated algorithms for the solution of linear problems. The physical meaning of the solution for any linear problem is clear on an intuitive level. The particularity of the linear system does not play an essential role. However, if we want to deal with real situations, we must take into account two new elements—non-linearity and noise. Non-linearity leads to incredible complications in solving technique. The combination of non-linearity with noise complicates the situation even more. In attempts to predict the behavior of such systems, the most refined intuition fails. The stochastic resonance effect represents an example of the paradoxical behavior of non-linear systems under influence of noise. The term “stochastic resonance” unites a group of phenomena for which the growth of disorder (noise amplitude) upon input into a non-linear system leads under certain conditions to an increase of order on the output. Quantitatively, the effect manifests in the fact that such integral system characteristics as gain constant, noise-to-signal ratio have a clearly marked maximum at some optimal noise level. At the same time, the system entropy reaches a minimum, giving evidence of noise-induced order growth.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Benzi, R., Sutera, A., Vulpiani, A.: J. Phys. A 14, L453–L457 (1981)
Benzi, R., Parisi, G., Sutera, A., Vulpiani, A.: Tellus 34, 10–16 (1982)
Nicolis, C., Nicolis, G.: Tellus 33, 225–237 (1981)
Nicolis, C.: Tellus 34, 1–9 (1982)
Gang, H., Ditzinger, T., Ning, C.Z., Haken, H.: Phys. Rev. Lett. 71, 807–810 (1993)
Kramers, H.: Physica (Utrecht) 7, 284–312 (1940)
Anishenko, V.C., Neiman, A.B., Moss, F., Shimansky-Gaier, L.: UFN 169, 7–39 (1999)
Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Rev. Mod. Phys. 70, 223–287 (1998)
Gross, D.: Lect. Notes Phys. 117, 81 (1980)
Frobrich, P., Lipperheide, R.: Theory of Nuclear Reactions. Oxford University Press, Oxford (1996)
Frobrich, P., Gontchar, I.: Phys. Rep. 292, 131–237 (1998)
Gardiner, C.W.: Handbook of Stochastic Methods. Springer Series in Synergetics, vol. 13, 2nd edn. Springer, Berlin/Heidelberg (1985)
Nyquist, H.: Phys. Rev. 32, 110–113 (1928)
Callen, H., Welton, T.: Phys. Rev. 83, 34–40 (1951)
Kubo, R.: J. Phys. Soc. Jpn. 12, 570–586 (1957)
Langevin, P.: C. R. Acad. Sci. Paris 146, 530–533 (1908)
McNamara, B., Wiesenfeld, K.: Phys. Rev. A 39, 4854–4869 (1989)
Landau, L.D., Lifshitz, E.M.: Statistical Physics. Pergamon Press, Oxford (1980)
Jung, P., Hänggi, P.: Europhys. Lett. 8, 505–510 (1989)
Zhiglo, A.V.: Probl. Atom. Sci. Technol. 6, 251–254 (2001)
Anishchenko, V.S., Neiman, A.V., Safanova, M.A.: J. Stat. Phys. 70, 183–196 (1993)
Anishenko, V.S.: JETF Lett. 10, 629–633 (1984)
Covey, C.: Sci. Am. 250, 42–50 (1984)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bolotin, Y., Tur, A., Yanovsky, V. (2017). Stochastic Resonance. In: Chaos: Concepts, Control and Constructive Use. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-42496-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-42496-5_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42495-8
Online ISBN: 978-3-319-42496-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)