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Stochastic Resonance and Its Precursors

  • M. I. Dykman
  • D. G. Luchinsky
  • R. Mannella
  • P. V. E. McClintock
  • N. D. Stein
  • N. G. Stocks
Part of the Institute for Nonlinear Science book series (INLS)

Abstract

We review some basic theoretical ideas and revealing experimental observations on stochastic resonance, a phenomenon in which the signal and/or signal-to-noise ratio in a nonlinear system increases with increasing intensity of noise. These ideas and results are related to those known from earlier work in condensed matter physics.

Keywords

Noise Intensity Stochastic Resonance Ring Laser Planktonic Foraminifera Periodic Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. 60, 2626 (1988).ADSCrossRefGoogle Scholar
  2. [2]
    M.I. Dykman, A.L. Velikovich, G.R Golubev, D.G. Luchinsky, and S.V. Tsuprikov, JETP Lett. 53, 193 (1991).ADSGoogle Scholar
  3. [3]
    L. Gammaitoni, M. Martinelli, L. Pardi, and S. Santucci, Phys. Rev. Lett. 67, 1799(1991).ADSCrossRefGoogle Scholar
  4. [4]
    A. Simon and A. Libchaber, Phys. Rev. Lett. 68, 3375 (1992).ADSCrossRefGoogle Scholar
  5. [5]
    S.T. Vohra and F. Bucholtz, J. Stat. Phys. 70, 413 (1993).ADSCrossRefGoogle Scholar
  6. [6]
    E. Ippen, J. Linder, and W.L. Ditto, J. Stat. Phys. 70, 437 (1993).ADSCrossRefGoogle Scholar
  7. [7]
    A. Fioretti, R. Mannella, L. Guidoni, L. Fronzoni, and E. Arimondo, J. Stat. Phys. 70, 799(1993).CrossRefGoogle Scholar
  8. [8]
    A. Hibbs, E.W. Jacobs, J. Bekkedahl, A. Bulsara, and F. Moss, Proceedings of the AIP Conference on Noise in Physical Systems and 1/f Fluctuations (American Institute of Physics, New York, 1993), p. 720.CrossRefGoogle Scholar
  9. [9]
    R.N. Mantegna and B. Spagnolo, Phys. Rev. 49, R1792 (1994).ADSGoogle Scholar
  10. [10]
    A. Longtin, A. Bulsara, and F. Moss, Phys. Rev. Lett. 67, 656 (1991).ADSCrossRefGoogle Scholar
  11. [11]
    F. Moss and A. Bulsara, Proceedings of the AIP Conference on Noise in Physical Systems and 1/f Fluctuations (American Institute of Physics, New York, 1993), p. 703, and references therein.CrossRefGoogle Scholar
  12. [12]
    J.K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, Nature 365, 337 (1993).ADSCrossRefGoogle Scholar
  13. [13]
    S. Fauve and F. Heslot, Phys. Lett. A 97, 5 (1983).ADSCrossRefGoogle Scholar
  14. [14a]
    G. Debnath, T. Zhou, and F. Moss, Phys. Rev. A 39, 4323 (1989)ADSCrossRefGoogle Scholar
  15. [14b]
    L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, Phys. Rev. Lett. 62, 349 (1989)ADSCrossRefGoogle Scholar
  16. [14c]
    G. Vemuri and R. Roy, Phys Rev. A 39, 4668 (1989)ADSCrossRefGoogle Scholar
  17. [14d]
    C. Presilla, F. Marchesoni, and L. Gammaitoni, Phys. Rev. A 40, 2105 (1989).ADSCrossRefGoogle Scholar
  18. [15a]
    M.I. Dykman, R. Mannella, P.V.E. McClintock, and N.G. Stocks, Phys. Rev. Lett. 65, 2606 (1990)ADSCrossRefGoogle Scholar
  19. [15b]
    M.I. Dykman, P.V.E. McClintock, R. Mannella, and N.G. Stocks, JETP Lett. 52, 144 (1990).ADSGoogle Scholar
  20. [16]
    T. Zhou, F. Moss, and P. Jung, Phys. Rev. A 42, 3161 (1990).ADSCrossRefGoogle Scholar
  21. [17]
    V.S. Anischenko, M.A. Safonova, and L.O. Chua, Int. J. Bifurcations Chaos 2, 397 (1992).CrossRefGoogle Scholar
  22. [18]
    N.G. Stocks, P.V.E. McClintock, and S.M. Soskin, Europhys. Lett. 21, 395 (1993)ADSCrossRefGoogle Scholar
  23. [18]
    N.G. Stocks, N.D. Stein, and P.V.E. McClintock, J. Phys. A 26, L385 (1993).ADSCrossRefGoogle Scholar
  24. [19]
    L.B. Kiss, Z. Gingl, Z. Márton, J. Kertész, F. Moss, G. Schmera, and A. Bulsara, J. Stat. Phys. 70, 451 (1993).ADSCrossRefGoogle Scholar
  25. [20a]
    T.L. Carroll and L.M. Pecora, Phys. Rev. Lett. 70, 576 (1993)ADSCrossRefGoogle Scholar
  26. [20b]
    T.L. Carroll and L.M. Pecora, Phys. Rev. E 47, 3941(1993).ADSCrossRefGoogle Scholar
  27. [21a]
    M.I. Dykman, D.G. Luchinsky, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, JETP Lett. 58, 145 (1993)ADSGoogle Scholar
  28. [21b]
    M.I. Dykman, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, Phys. Rev. E 49, 1198 (1994).ADSCrossRefGoogle Scholar
  29. [22]
    K. Wiesenfeld, D. Pierson, E. Pantazelou, C. Dames, and F. Moss, Phys. Rev. Lett. 72, 2125 (1994).ADSCrossRefGoogle Scholar
  30. [23]
    Special issue of J. Stat. Phys. 70, Nos. 1, 2 (1993).Google Scholar
  31. [24]
    Special issue of Nuovo Cimento D 17 (1995). This issue contains an extended version of the present chapter (p. 661).Google Scholar
  32. [25a]
    R. Löfstedt and S.N. Coppersmith, Phys. Rev. Lett. 72, 1947 (1994)ADSCrossRefGoogle Scholar
  33. [25b]
    G.B. Alers, N.O. Birge, and B. Golding, to be published.Google Scholar
  34. [26a]
    E.K. Sadykov, J. Phys.: Condens. Matter 4, 3295 (1992)ADSCrossRefGoogle Scholar
  35. [26b]
    Yu.L. Raikher and V.I. Stepanov, J. Phys.: Condens. Matter 6, 4137 (1994).ADSCrossRefGoogle Scholar
  36. [27]
    M.I. Dykman, G.P. Golubev, D.G. Luchinsky, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, Phys. Rev. E 49, 1935 (1994).ADSCrossRefGoogle Scholar
  37. [28]
    R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 14, L453 (1981).MathSciNetADSCrossRefGoogle Scholar
  38. [29]
    C. Nicolis, Tellus 34, 1 (1982).MathSciNetADSCrossRefGoogle Scholar
  39. [30]
    R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, Tellus 34, 10 (1982).ADSCrossRefGoogle Scholar
  40. [31]
    J.D. Hays, J. Imbrie, and N.J. Shackleton, Science 194, 1121 (1976).ADSCrossRefGoogle Scholar
  41. [32]
    H. Kramers, Physica 7, 284 (1940).MathSciNetADSzbMATHCrossRefGoogle Scholar
  42. [33]
    M.I. Dykman, R. Mannella, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, Phys. Rev. E 47, 1629 (1993).ADSCrossRefGoogle Scholar
  43. [34]
    B. McNamara and K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989).ADSCrossRefGoogle Scholar
  44. [35]
    L.D. Landau and E.M. Lifshitz, Statistical Physics, 3rd ed., Part 1 (Pergamon, New York, 1980).Google Scholar
  45. [36]
    M.I. Dykman, D.G. Luchinsky, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, Phys. Rev. A 46, R1713 (1992).ADSCrossRefGoogle Scholar
  46. [37a]
    M.I. Dykman and M.A. Krivoglaz, in Soviet Physics Reviews, edited by I.M. Khalatnikov (Harwood, New York, 1984) vol. 5, p. 265Google Scholar
  47. [37b]
    M.I. Dykman and P.V.E. McClintock, Physica D 58, 10 (1992).ADSCrossRefGoogle Scholar
  48. [38a]
    S.M. Soskin, Physica A 180, 386 (1992)ADSCrossRefGoogle Scholar
  49. [38b]
    N.G. Stocks, N.D. Stein, S.M. Soskin, and P.V.E. McClintock, J. Phys. A 25, L1119 (1992).ADSCrossRefGoogle Scholar
  50. [39]
    P. Debye, Polar Molecules (Dover, Mineola, NY, 1929).zbMATHGoogle Scholar
  51. [40]
    A.S. Nowick and B.S. Berry, Anelastic Relaxation in Crystalline Solids (Academic Press, New York, 1972).Google Scholar
  52. [41]
    C. Wert and C. Zener, Phys. Rev. 76, 1169 (1949).ADSCrossRefGoogle Scholar
  53. [42a]
    J.L. Snoek, Physica 8, 711 (1941)ADSCrossRefGoogle Scholar
  54. [42b]
    J.L. Snoek, Physica 9, 862 (1942).ADSCrossRefGoogle Scholar
  55. [43]
    M.I. Dykman, R. Mannella, P.V.E. McClintock, and N.G. Stocks, Phys. Rev. Lett. 68, 2985 (1992).ADSCrossRefGoogle Scholar
  56. [44]
    R.F. Fox and Y. Lu, Phys. Rev. E 48, 3390 (1993).ADSCrossRefGoogle Scholar
  57. [45]
    M. Morillo and J. Gòmez-Ordòñez, Phys. Rev. Lett. 71, 9 (1993).ADSCrossRefGoogle Scholar
  58. [46]
    P. Jung and P. Hänggi, Europhys. Lett. 8, 505 (1989).ADSCrossRefGoogle Scholar
  59. [47]
    H.M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, New York, 1985).Google Scholar
  60. [48]
    M.I. Dykman and M.A. Krivoglaz, Sov. Phys. JETP 50, 30 (1979).ADSGoogle Scholar
  61. [49a]
    M.I. Dykman, Phys. Rev. A 42, 2020 (1990)MathSciNetADSCrossRefGoogle Scholar
  62. [49b]
    M.I. Dykman and K. Lindenberg, in Contemporary Problems of Statistical Physics, edited by G. Weiss (SIAM, Philadelphia, 1994), p. 41CrossRefGoogle Scholar
  63. [49c]
    the analysis of the topology of large fluctuations and of the escape probabilities for periodically driven systems has been done by M.I. Dykman and V.N. Smelyanskiy (unpublished).Google Scholar
  64. [50a]
    J.F. Luciani and A.D. Verga, Europhys. Lett. 4, 255 (1987)ADSCrossRefGoogle Scholar
  65. [50b]
    M.M. Klosek-Dygas, B.J. Matkowsky, and Z. Schuss, SIAM J. Appl. Math 48, 425 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  66. [50c]
    A.J. Bray and A.J. McKane, Phys. Rev. Lett. 62, 493 (1989)ADSCrossRefGoogle Scholar
  67. [50d]
    S.LB. Einchcomb and A.J. McKane, Phys. Rev. E 49, 259 (1994)ADSCrossRefGoogle Scholar
  68. [50e]
    K. Lindenberg, B.J. West, and G.P Tsironis, Rev. Solid State Sci. 3, 143 (1989).Google Scholar
  69. [51a]
    N.G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1990)Google Scholar
  70. [51b]
    H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer-Verlag, Berlin, 1989).Google Scholar
  71. [52a]
    G. Hu, H. Haken, and C.Z. Ning, Phys. Lett. A 172 21 (1992)ADSCrossRefGoogle Scholar
  72. [52b]
    M.I. Dykman, H. Haken, Hu Gang, D.G. Luchinsky, P.V.E. McClintock, C.Z. Ning, N.D. Stein, and N.G. Stocks, Phys. Lett. A 180, 332 (1993).ADSCrossRefGoogle Scholar
  73. [53]
    P. Hänggi and H. Thomas, Phys. Rep. 88, 207 (1982).MathSciNetADSCrossRefGoogle Scholar
  74. [54]
    Yu. Kagan and A.J. Leggett, eds., Quantum Tunnelling in Condensed Media (Elsevier, Amsterdam, 1992).Google Scholar
  75. [55a]
    R.S. Maier and D.L. Stein, Phys. Rev. Lett. 69, 3691 (1992)Google Scholar
  76. [55b]
    R.S. Maier and D.L. Stein, Phys. Rev. E 48, 931 (1993)ADSCrossRefGoogle Scholar
  77. [55c]
    V. A. Chinarov, M. I. Dykman, and V. N. Smelyanskiy, Phys. Rev. E 47, 2448 (1993)ADSCrossRefGoogle Scholar
  78. [55d]
    R.S. Maier and D.L. Stein, Phys. Rev. Lett. 71, 1783 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

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

There are no affiliations available

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