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Noise-Induced Linearization and Delinearization

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

Abstract

The change of the character of the response of a nonlinear system to a low-frequency periodic field induced by external noise is analyzed by means of analog electronic simulation and theoretically. In general, noise of sufficient intensity linearizes the response. For certain parameter ranges, however, an increase in the noise intensity can sometimes have the opposite effect and is shown to delinearize the response. The physical origins of these contrary behaviors are discussed.

Keywords

Noise Intensity Stochastic Resonance External Noise Periodic Force Weak Noise 
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]
    G. Nicolis and I. Prigogine, Exploring Complexity: an Introduction (Freeman, New York, 1989).Google Scholar
  2. [2]
    J.M.T. Thompson and H.B. Stewart, Nonlinear Dynamics and Chaos (Wiley, New York, 1986).zbMATHGoogle Scholar
  3. [3]
    M.I. Dykman, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, “Stochastic Resonance”, and references therein. In this volume, pp xx-yy.Google Scholar
  4. [4]
    W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer-Verlag, Berlin, 1984).zbMATHGoogle Scholar
  5. [5]
    K. Vogel, H. Risken, W. Schleich, M. James, F. Moss, R. Mannella, and P.V.E. McClintock, J. Appl. Phys. 62, 721 (1987).ADSCrossRefGoogle Scholar
  6. [6]
    S. Kai, “Electrohydrodynamic Instability of Nematic Liquid Crystals: Growth Process and Influence of Noise ”in Noise in Nonlinear Dynamical Systems, vol. 3, edited by F. Moss and P.V.E. McClintock, (Cambridge University Press, Cambridge, 1989), pp 22–76.CrossRefGoogle Scholar
  7. [7]
    R.J. Deissler, J. Stat. Phys. 54, 1459 (1989).MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    A.J. Mandell and K.A. Selz, J. Stat. Phys. 70, 355 (1993).ADSzbMATHCrossRefGoogle Scholar
  9. [9]
    M.I. Dykman, R. Mannella, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, Phys. Rev. A 42, 7041 (1990).ADSCrossRefGoogle Scholar
  10. [10]
    L.D. Landau and E.M. Lifshitz, Statistical Physics, 3rd Ed. (Pergamon, Oxford, 1980).Google Scholar
  11. [11]
    M.I. Dykman, P.V.E. McClintock, R. Mannella, and N.G. Stocks, Sov. Phys. J.E.T.P.Lett. 52, 141 (1990).ADSGoogle Scholar
  12. [12]
    M.I. Dykman, R. Mannella, P.V.E. McClintock, and N.G. Stocks, Phys. Rev. Lett. 68, 2985 (1992).ADSCrossRefGoogle Scholar
  13. [13]
    M.I. Dykman, R. Mannella, P.V.E. McClintock, N.D. Stein, and N.G. Stocks, Phys. Rev. E 47, 1629 (1993).ADSCrossRefGoogle Scholar
  14. [14]
    L. Fronzoni, “Analogue Simulations of Stochastic Processes by Means of Minimum Component Electronic Devices,” in Noise in Nonlinear Dynamical Systems, vol. 3, edited by F. Moss and P.V.E. McClintock, (Cambridge University Press, Cambridge, 1989), pp. 222–242.CrossRefGoogle Scholar
  15. [15]
    P.V.E. McClintock and F. Moss, “Analogue Techniques for the Study of Problems in Stochastic Nonlinear Dynamics,” in Noise in Nonlinear Dynamical Systems, vol. 3, edited by F. Moss and P.V.E. McClintock, (Cambridge University Press, Cambridge, 1989), pp. 243–274.CrossRefGoogle Scholar
  16. [16]
    S.M. Soskin, Physica A 180, 386 (1992).ADSCrossRefGoogle Scholar
  17. [17]
    N.G. Stocks, P.V.E. McClintock, and S.M. Soskin, Europhys. Lett. 21, 395 (1993).ADSCrossRefGoogle Scholar
  18. [18]
    N.G. Stocks, N.D. Stein, and P.V.E. McClintock, J. Phys. A: Math Gen. 26, L385 (1993).ADSCrossRefGoogle Scholar
  19. [19]
    M.I. Dykman, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, H.E. Short, N.D. Stein, and N.G. Stocks, “Noise-Enhanced Two-Photon Absorption by a Nonlinear Oscillator,” in preparation.Google Scholar
  20. [20]
    M.I. Dykman and M.A. Krivoglaz, Phys. Status Solidi B 48, 497 (1971).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

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

There are no affiliations available

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