Abstract
It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found, and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; and (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated.
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References
F. Moss, Stochastic resonance: From the ice ages to the monkey's ear, inSome Problems in Statistical Physics, G. H. Weiss, ed. (SIAM, Philadelphia, 1992).
M. I. Dykman, G. P. Golubev, D. G. Luchinsky, A. L. Velikovich, and S. V. Tsuprikov,Sov. Phys. JETP Lett. 53:193 (1991).
M. I. Dykman, R. Mannella, P. V. E. McClintock, and N. G. Stocks,Phys. Rev. Lett. 65:2606 (1990).
M. I. Dykman, R. Mannella, P. V. E. McClintock, and N. G. Stocks,Sov. Phys. JETP Lett. 52:141 (1990).
M. I. Dykman, R. Mannella, P. V. E. McClintock, and N. G. Stocks,Phys. Rev. Lett. 68:2985 (1992).
M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks,J. Stat. Phys., this issue.
L. D. Landau and E. M. Lifshitz,Statistical Physics, 3rd ed. (Pergamon Press, New York, 1980).
M. I. Dykman, R. Mannella, P. V. E. McClintock, S. M. Soskin, and N. G. Stocks,Phys. Rev. A 42:7041 (1990).
S. M. Soskin,Physica A 155:401 (1989);180:386 (1992).
N. G. Stocks, P. V. E. McClintock, and S. M. Soskin, Observation of zero-dispersion peaks in the fluctuation spectrum of an underdamped single-well oscillator, to be published.
L. Fronzoni, inNoise in Nonlinear Dynamical Systems, F. Moss and P. V. E. McClintock, eds. (Cambridge University Press, Cambridge, 1989), Vol.3, p. 222; P. V. E. McClintock and F. Moss, inNoise in Nonlinear Dynamical Systems, F. Moss and P. V. E. McClintock, eds. (Cambridge University Press, Cambridge, 1989), Vol. 3, p. 243; N. G. Stocks, Experiments in stochastic nonlinear dynamics, Ph.d. thesis, Lancaster (1990).
M. I. Dykman, R. Mannella, P. V. E. McClintock, S. M. Soskin, and N. G. Stocks,Phys. Rev. A 43:1701 (1991).
B. McNamara, K. Wiesenfeld, and R. Roy,Phys. Rev. Lett. 60:2626 (1988).
L. D. Landau and E. M. Lifshitz,Mechanics (Pergamon Press, London, 1976).
H. M. Gibbs,Optical Bistability: Controlling Light with Light (Academic Press, New York, 1985); P.D. Drummond and D. F. Walls,J. Phys. A 13:725 (1980); C. Flytzanis and C. L. Tang,Phys. Rev. Lett. 45:441 (1980); J. A. Goldstone and E. Garmire,Phys. Rev. Lett. 53:910 (1984).
G. Gabrielse, H. Dehmelt, and W. Keils,Phys. Rev. Lett. 54:537 (1985).
M. I. Dykman and M. A. Krivoglaz,Sov. Phys. JETP 50:30 (1979); M. I. Dykman and M. A. Krivoglaz, inSoviet Physics Reviews, I. M. Khalatnikov, ed. (Harwood, New York, 1984), Vol. 5, p. 265.
M. I. Dykman, M. A. Krivoglaz, and S. M. Soskin, inNoise in Nonlinear Dynamical Systems, F. Moss and P. V. E. McClintock, eds. (Cambridge University Press, Cambridge, 1989), Vol. 2, p. 347.
M. I. Dykman and V. N. Smelyanski,Phys. Rev. A 41:3090 (1990).
M. I. Dykman, R. Mannella, P. V. E. McClintock, and N. G. Stocks,Phys. Rev. Lett. 65:48 (1990).
R. Bonifacio and L. A. Lugiato,Phys. Rev. Lett. 40:1023 (1978); L. A. Lugiato, inProgress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, p. 69.
M. I. Dykman, R. Mannella, P. V. E. McClintock, F. Moss, and S. M. Soskin,Phys. Rev. A 37:1303 (1988).
M. I. Dykman, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, High frequency stochastic resonance for periodic attractors, to be published.
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Dykman, M.I., Luchinsky, D.G., Mannella, R. et al. Nonconventional stochastic resonance. J Stat Phys 70, 479–499 (1993). https://doi.org/10.1007/BF01053983
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DOI: https://doi.org/10.1007/BF01053983