Il Nuovo Cimento D

, Volume 17, Issue 7–8, pp 661–683 | Cite as

Stochastic resonance in perspective

  • M. I. Dykman
  • D. G. Luchinsky
  • R. Mannella
  • P. V. E. McClintock
  • N. D. Stein
  • N. G. Stocks


We outline the historical development of stochastic resonance (SR), a phenomenon in which the signal and/or the signal-to-noise ratio in a nonlinear system increase with increasing intensity of noise. We discuss basic theoretical ideas explaining and describing SR, and we review some revealing experimental data that place SR within the wider context of statistical physics. We emphasize the close relationship of SR to some effects that are well known in condensed-matter physics.

PACS 87.10

General, theoretical, and mathematical biophysics (including logic of biosystems, quantum biology and relevant aspects of thermodynamics, information theory, cybernetics and bionics) 

PACS 05.40

Fluctuation phenomena, random processes, and Brownian motion 

PACS 02.50

Probability theory, stochastic processes, and statistics 

PACS 01.30.Cc

Conference proceedings 


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  1. [1]
    Special issue ofJ. Stat. Phys.,70, no. 1/2 (1993).Google Scholar
  2. [2]
    Simon A. andLibchaber A.,Phys. Rev. Lett.,68 (1992) 3375.CrossRefADSGoogle Scholar
  3. [3]
    Stocks N. G., McClintock P. V. E. andSoskin S. M.,Europhys. Lett.,21 (1993) 395;Stocks N. G., Stein N. D. andMcClintock P. V. E.,J. Phys. A,26 (1993) L385.ADSGoogle Scholar
  4. [4]
    Hibbs A., Jacobs E. W., Bekkedahl J., Bulsara A. andMoss F.,Proceedings of the AIP Conference on Noise in Physical Systems and 1/f Fluctuations (AIP Press, New York, N.Y.) 1993, p. 720.Google Scholar
  5. [5]
    Douglass J. K., Wilkens L., Pantazelou E. andMoss F.,Nature,365 (1993) 337.CrossRefADSGoogle Scholar
  6. [6]
    Carroll T. L. andPecora L. M.,Phys. Rev. Lett.,70 (1993) 576;Phys. Rev. E,47 (1993) 3941.CrossRefADSGoogle Scholar
  7. [7]
    Dykman M. I., Luchinsky D. G., McClintock P. V. E., Stein N. D. andStocks N. G.,JETP Lett.,58 (1993) 145;Dykman M. I., Luchinsky D. G., Mannella R., McClintock P. V. E., Stein N. D. andStocks N. G.,Phys. Rev. E,49 (1994) 1198.ADSGoogle Scholar
  8. [18] a)
    Löfstedt R. andCoppersmith S. N.,Phys. Rev. Lett.,72 (1994) 1947;b)Alers G. B., Birge N. O. andGolding B., to be published.CrossRefADSGoogle Scholar
  9. [9]
    Wiesenfeld K., Pierson D., Pantazelou E., Dames C. andMoss F.,Phys. Rev. Lett.,72 (1994) 2125.CrossRefADSGoogle Scholar
  10. [10]
    Mantegna R. N. andSpagnolo B.,Phys. Rev. E,49 (1994) R1792.CrossRefADSGoogle Scholar
  11. [11]
    Dykman M. I., Golubev G. P., Luchinsky D. G., McClintock P. V. E., Stein N. D. andStocks N. G.,Phys. Rev. E,49 (1994) 1935.CrossRefADSGoogle Scholar
  12. [12]
    Benzi R., Sutera A. andVulpiani A.,J. Phys. A,14 (1981) L453.MathSciNetCrossRefADSGoogle Scholar
  13. [13]
    Nicolis C.,Tellus,34 (1982) 1.MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    Benzi R., Parisi G., Sutera A. andVulpiani A.,Tellus,34 (1982) 10.ADSGoogle Scholar
  15. [15]
    Fauve S. andHeslot F.,Phys. Lett. A,97 (1983) 5.CrossRefADSGoogle Scholar
  16. [16]
    McNamara B., Wiesenfeld K. andRoy R.,Phys. Rev. Lett.,60 (1988) 2626.CrossRefADSGoogle Scholar
  17. [17]
    Hays J. D., Imbrie John andShackleton N. J.,Science,194 (1976) 1121.ADSGoogle Scholar
  18. [18]
    Milankovitch M., K. Serb. Akad. Beogr. Spec. Publ. (1941) 132.Google Scholar
  19. [19]
    Kramers H.,Physica,7 (1940) 284.zbMATHMathSciNetCrossRefADSGoogle Scholar
  20. [20]
    McNamara B. andWiesenfeld K.,Phys. Rev. A,39 (1989) 4854.CrossRefADSGoogle Scholar
  21. [21]
    Dykman M. I., Mannella R., McClintock P. V. E., Stein N. D. andStocks N. G.,Phys. Rev. E.,47 (1993) 1629.CrossRefADSGoogle Scholar
  22. [22]
    Debnath G., Zhou T. andMoss F.,Phys. Rev. A,39 (1989) 4323;Gammaitoni L., Marchesoni F., Menichella-Saetta E. andSantucci S.,Phys. Rev. Lett.,62 (1989) 349;Vemuri G. andRoy R.,Phys. Rev. A,39 (1989) 4668;Presilla C., Marchesoni F. andGammaitoni L.,Phys. Rev. A,40 (1989) 2105.CrossRefADSGoogle Scholar
  23. [23]
    Dykman M. I., Mannella R., McClintock P. V. E. andStocks N. G.,Phys. Rev. Lett.,65 (1990) 2606;Dykman M. I., McClintock P. V. E., Mannella R. andStocks N. G.,JETP Lett.,52 (1990) 144.CrossRefADSGoogle Scholar
  24. [24]
    Anischenko V. S., Safonova M. A. andChua L. O.,Int. J. Bifurcations Chaos,2 (1992) 397.CrossRefGoogle Scholar
  25. [25]
    Dykman M. I., Velikovich A. L., Golubev G. P., Luchinsky D. G. andTsuprikov S. V.,JETP Lett.,53 (1991) 193.ADSGoogle Scholar
  26. [26]
    Fioretti A., Mannella R., Guidoni L., Fronzoni L. andArimondo E.,J. Stat. Phys.,70 (1993) 799.CrossRefGoogle Scholar
  27. [27]
    Ippen E., Linder J. andDitto W. L.,J. Stat Phys.,70 (1993) 437.CrossRefADSGoogle Scholar
  28. [28]
    Gammaitoni L., Martinelli M., Pardi L. andSantucci S.,Phys. Rev. Lett.,67 (1991) 1799.CrossRefADSGoogle Scholar
  29. [29]
    Sadykov E. K.,J. Phys.: Condens. Matter,4 (1992) 3295;Raikher Yu. L. andStepanov V. I.,J. Phys.: Condens. Matter,6 (1994) 4137.CrossRefADSGoogle Scholar
  30. [30]
    Vohra S. T. andBucholtz F.,J. Stat. Phys.,70 (1993) 413.CrossRefADSGoogle Scholar
  31. [31]
    Longtin A., Bulsara A. andMoss F.,Phys. Rev. Lett.,67 (1991) 656.CrossRefADSGoogle Scholar
  32. [32]
    Moss F. andBulsara A.,Proceedings of the AIP Conference on Noise in Physical Systems and 1/f Fluctuations (AIP Press, New York, N.Y.) 1993, p. 703, and references therein.Google Scholar
  33. [33]
    Longtin A.,J. Stat. Phys.,70 (1993) 309;Chialvo D. R. andApkarian A. V.,J. Stat. Phys.,70 (1993) 375.zbMATHCrossRefADSGoogle Scholar
  34. [34]
    Bulsara A. R. andSchmera G.,Phys. Rev. E,47 (1993) 3734.CrossRefADSGoogle Scholar
  35. [35]
    Landau L. D. andLifshitz E. M.,Statistical Physics, 3rd edition, Part 1 (Pergamon, New York, N.Y.) 1980.Google Scholar
  36. [36]
    Dykman M. I., Luchinsky D. G., McClintock P. V. E., Stein N. D. andStocks N. G.,Phys. Rev. A,46 (1992) R1713.CrossRefADSGoogle Scholar
  37. [37]
    Dykman M. I. andKrivoglaz M. A., inSov. Phys. Rev., edited byI. M. Khalatnikov, Vol. 5 (Harwood, New York, N.Y.) 1984, p. 265;Dykman M. I. andMcClintock P. V. E.,Physica D,58 (1992) 10.Google Scholar
  38. [38]
    Soskin S. M.,Physica A,180 (1992) 386;Stocks N. G., Stein N. D., Soskin S. M. andMcClintock P. V. E.,J. Phys. A,25 (1992) L1119.CrossRefADSGoogle Scholar
  39. [39]
    Kiss L. B., Gingl Z., Márton Z., Kertész J., Moss F., Schmera G. andBulsara A.,J. Stat. Phys.,70 (1993) 451.CrossRefADSGoogle Scholar
  40. [40]
    Debye P.,Polar Molecules (Dover Publications, Inc.) 1929.Google Scholar
  41. [41]
    Nowick A. S. andBerry B. S.,Anelastic Relaxation in Crystalline Solids (Academic Press, New York) 1972.Google Scholar
  42. [42]
    Wert C. andZener C.,Phys. Rev.,76 (1949) 1169.CrossRefADSGoogle Scholar
  43. [43]
    Snoek J. L.,Physica,8 (1941) 711;9 (1942) 862.CrossRefADSGoogle Scholar
  44. [44]
    Dykman M. I., Mannella R., McClintock P. V. E. andStocks N. G.,Phys. Rev. Lett.,68 (1992) 2985.CrossRefADSGoogle Scholar
  45. [45]
    Fox R. F. andLu Y.,Phys. Rev. E,48 (1993) 3390.CrossRefADSGoogle Scholar
  46. [46]
    Gibbs H. M.,Optical Bistability: Controlling Light with Light (Academic Press, New York, N.Y.) 1985.Google Scholar
  47. [47]
    Dykman M. I. andKrivoglaz M. A.,Sov. Phys. JETP,50 (1979) 30.ADSGoogle Scholar
  48. [48]
    Dykman M. I.,Phys. Rev. A,42 (1990) 2020;Dykman M. I. andLindenberg K., inContemporary Problems of Statistical Physics, edited byG. Weiss (SIAM, Philadelphia) 1994, p. 41.MathSciNetCrossRefADSGoogle Scholar
  49. [49]
    Luciani J. F. andVerga A. D.,Europhys. Lett.,4 (1987) 255;Klosek-Dygas M. M., Matkowsky B. J. andSchuss Z.,SIAM J. Appl. Math.,48 (1988) 425;Bray A. J. andMcKane A. J.,Phys. Rev. Lett.,62 (1989) 493;Einchcomb S. J. B. andMcKane A. J.,Phys. Rev. E,49 (1994) 259;Lindenberg K., West B. J. andTsironis G. P.,Rev. Solid State Sci., 3 (1989) 143.ADSGoogle Scholar
  50. [50]
    van Kampen N. G.,Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam) 1990;Risken H.,The Fokker-Planck Equation (Springer, Berlin) 1989, 2nd edition.Google Scholar
  51. [51] a)
    Hu G., Haken H. andNing C. Z.,Phys. Lett. A,172 (1992) 21;b)Dykman M. I., Haken H., Hu Gang, Luchinsky D. G., McClintock P. V. E., Ning C. Z., Stein N. D. andStocks N. G.,Phys. Lett. A,180 (1993) 332.CrossRefADSGoogle Scholar
  52. [52]
    Hänggi P. andThomas H.,Phys. Rep.,88 (1982) 207.MathSciNetCrossRefADSGoogle Scholar
  53. [53]
    Morillo M. andGòmez-Ordòñez J.,Phys. Rev. Lett.,71 (1993) 9.CrossRefADSGoogle Scholar
  54. [54]
    Jung P. andHänggi P.,Europhys. Lett.,8 (1989) 505.ADSGoogle Scholar
  55. [55]
    Neiman A. andSchimansky-Geier L.,Phys. Rev. Lett.,72 (1994) 2988.CrossRefADSGoogle Scholar
  56. [56]
    Zhou T., Moss F. andJung P.,Phys. Rev. A,42 (1990) 3161.CrossRefADSGoogle Scholar
  57. [57]
    Landau L. D. andLifshitz E. M.,Mechanics (Pergamon, London) 1976.Google Scholar
  58. [58]
    Kagan Yu. andLeggett A. J. (Editors),Quantum Tunnelling in Condensed Media (Elsevier, Amsterdam) 1992.Google Scholar
  59. [59]
    Maier R. S. andStein D. L.,Phys. Rev. Lett.,69 (1992) 3691;Phys. Rev. E,48 (1993) 931;Chinarov V. A., Dykman M. I. andSmelyanskiy V. N.,Phys. Rev. E,47 (1993) 2448;Maier R. S. andStein D. L.Phys. Rev. Lett.,171 (1993) 1783;Dykman M. I., Millonas M. andSmelyanskiy V. N.,Phys. Lett. A,195 (1994) 53.CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1995

Authors and Affiliations

  • M. I. Dykman
    • 1
  • D. G. Luchinsky
    • 2
  • R. Mannella
    • 3
  • P. V. E. McClintock
    • 4
  • N. D. Stein
    • 4
  • N. G. Stocks
    • 4
  1. 1.Department of Physics and AstronomyMichigan State UniversityEast LansingUSA
  2. 2.All Russian Research Institute for Metrological ServiceMoscowRussia
  3. 3.Dipartimento di FisicaUniversità di PisaPisaItaly
  4. 4.School of Physics and ChemistryLancaster UniversityLancasterUK

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