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Noise-Induced Synchronization and Stochastic Resonance in a Bistable System

  • Agnessa Kovaleva
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)

Abstract

We determine stochastic resonance and locking conditions for noise-induced interwell jumps in a bistable system. We demonstrate that the phenomena of stochastic resonance and synchronization are not contradictory and can be interpreted as the limit cases of hopping dynamics modulated by a weak signal. The boundary between the domains of synchronization and stochastic resonance is found as a function of the system parameters.

Key words

Stochastic systems synchronization stochastic resonance 

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References

  1. [1]
    B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869, 1989.Google Scholar
  2. [2]
    D.S. Broomhead, E.A. Luchinskaya, P.V.E. McClintock, and T. Mullin, eds., Stochastic and Chaotic Dynamics in the Lakes, American Institute of Physics, Melville, N.Y., 2000.Google Scholar
  3. [3]
    L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchezoni, “Stochastic resonance,” Reviews of Modern Physics, 70, 223–287, 1998.CrossRefGoogle Scholar
  4. [4]
    M. Freidlin and A. Wentzell, Random Perturbations of Dynamical Systems, 2nd ed. Springer-Verlag, Berlin., 1998.Google Scholar
  5. [5]
    M. Freidlin, “Quasi-deterministic approximation metastability and stochastic resonance,” Physica D 137, 313–332, 2000.MathSciNetGoogle Scholar
  6. [6]
    P. Imkeller, “Energy balance models — viewed from stochastic dynamics,” in: Stochastic Climate Models (P. Imkeller, and J. von Storch (Eds)), 1–27. Birkhauser-Verlag AG, Switzerland, 2000.Google Scholar
  7. [7]
    P. Imkeller and I. Pavljukevich, “Stochastic resonance in two-state Markov chains,” Archiv der Mathematik, 77, 107–115, 2001MathSciNetCrossRefGoogle Scholar
  8. [8]
    B. Shulgin, A. Neiman and V. Anishchenko, “Mean switching frequency locking in stochastic bistable systems driven by a periodic force,” Phys. Rev. Letters, 75, 4157–4160, 1995.CrossRefGoogle Scholar
  9. [9]
    M. Tretyakov, Numerical Studies of Stochastic Resonance, preprint nr 302, Weierstrass-Institute fur Angewandte Analysis and Stochastic, Berlin, 1997.Google Scholar
  10. [10]
    J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1986.Google Scholar
  11. [11]
    R. Knapp, G., Papanicolaou and B. White, “Nonlinearity and localization in one-dimensional random media,” in: Disorder and Nonlinearity (A.R. Bishop, ed.), 2–26. Springer-Verlag, Berlin, 1989.Google Scholar
  12. [12]
    H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory. Cambridge: The MIT Press, 1984.Google Scholar
  13. [13]
    G. Blankenship, and G. Papanicolaou, “Stability and control of stochastic systems with wide band perturbations,” SIAM J. Appl. Math. 34, 437–476, 1978.MathSciNetCrossRefGoogle Scholar
  14. [14]
    A. Kovaleva, “Higher orders approximations of the perturbation method for systems with random coefficients,” J. Appl. Math. Mech., 55, 612–619, 1991.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Agnessa Kovaleva
    • 1
  1. 1.Space Research InstituteRussian Academy of SciencesMoscowRussia

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