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Noise-Induced Synchronization and Stochastic Resonance in a Bistable System

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Part of the book series: Solid Mechanics and its Applications ((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.

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References

  1. B. McNamara and K. Wiesenfeld, “Theory of stochastic resonance,” Phys. Rev. A 39, 4854–4869, 1989.

    Google Scholar 

  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. L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchezoni, “Stochastic resonance,” Reviews of Modern Physics, 70, 223–287, 1998.

    Article  Google Scholar 

  4. M. Freidlin and A. Wentzell, Random Perturbations of Dynamical Systems, 2nd ed. Springer-Verlag, Berlin., 1998.

    Google Scholar 

  5. M. Freidlin, “Quasi-deterministic approximation metastability and stochastic resonance,” Physica D 137, 313–332, 2000.

    MathSciNet  Google Scholar 

  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. P. Imkeller and I. Pavljukevich, “Stochastic resonance in two-state Markov chains,” Archiv der Mathematik, 77, 107–115, 2001

    Article  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  9. M. Tretyakov, Numerical Studies of Stochastic Resonance, preprint nr 302, Weierstrass-Institute fur Angewandte Analysis and Stochastic, Berlin, 1997.

    Google Scholar 

  10. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1986.

    Google Scholar 

  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. 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. G. Blankenship, and G. Papanicolaou, “Stability and control of stochastic systems with wide band perturbations,” SIAM J. Appl. Math. 34, 437–476, 1978.

    Article  MathSciNet  Google Scholar 

  14. A. Kovaleva, “Higher orders approximations of the perturbation method for systems with random coefficients,” J. Appl. Math. Mech., 55, 612–619, 1991.

    Article  MATH  MathSciNet  Google Scholar 

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© 2005 Springer

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Kovaleva, A. (2005). Noise-Induced Synchronization and Stochastic Resonance in a Bistable System. In: Rega, G., Vestroni, F. (eds) IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics. Solid Mechanics and its Applications, vol 122. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3268-4_33

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  • DOI: https://doi.org/10.1007/1-4020-3268-4_33

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-3267-7

  • Online ISBN: 978-1-4020-3268-4

  • eBook Packages: EngineeringEngineering (R0)

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