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Issue 9, 2026
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1999

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Reviews of topical problems


Stochastic resonance: noise-enhanced order

 a,  b,  c,  d
a International Research Institute of Nonlinear Dynamics, Department of Physics, N.G. Chernyshevskii; Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russian Federation
b Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410071, Russian Federation
c Department of Physics and Astronomy, University of Missouri at St. Louis, St. Louis, MO, USA
d Humboldt University at Berlin, Invalidenstr. 110, Berlin, D-10115, Germany

Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed.

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Fulltext is also available at DOI: 10.1070/PU1999v042n01ABEH000444
PACS: 02.50.Ey, 05.40.+j, 05.45.+b, 87.70.+c
DOI: 10.1070/PU1999v042n01ABEH000444
URL: https://ufn.ru/en/articles/1999/1/c/
000078623600001
Citation: Anishchenko V S, Neiman A B, Moss F, Shimansky-Geier L "Stochastic resonance: noise-enhanced order" Phys. Usp. 42 7–36 (1999)
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Оригинал: Анищенко В С, Нейман А Б, Мосс Ф, Шиманский-Гайер Л «Стохастический резонанс как индуцированный шумом эффект увеличения степени порядка» УФН 169 7–38 (1999); DOI: 10.3367/UFNr.0169.199901c.0007

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