Skip to main content

Stochastic Resonances in Underdamped Bistable Systems

  • Conference paper
  • First Online:
Stochastic Processes in Physics, Chemistry, and Biology

Part of the book series: Lecture Notes in Physics ((LNP,volume 557))

Abstract

Underdamped bistable dynamical systems driven by both periodic and noisy forces show the typical phenomenon of Stochastic Resonance. Such a phe- nomenon, characterized by the increase in the periodic component of the system response as a function of the noise intensity, can be ascribed to two different mech- anisms which, under certain condition, can coexist resulting in a characteristic double maximum in the power spectral amplitude. The locations of these maxima correspond to matchings of deterministic and stochastic time-scales in the system thus supporting the use of the term resonances.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Benzi,, A. Sutera, A. Vulpiani; J. Phys. A14, L453 (1981). C. Nicolis, G. Nicolis; Tellus 33, 225 (1981).

    ADS  MathSciNet  Google Scholar 

  2. B. McNamara, K. Wiesenfeld, R. Roy; Phys. Rev. Lett. 60, 2626 (1988). J. Iannelli, A. Yariv, T. Chen, Y. Zhuang; Appl. Phys. Lett. 65, 1983 (1994).

    Article  ADS  Google Scholar 

  3. L. Gammaitoni, M. Martinelli, L. Pardi, S. Santucci; Phys. Rev. Lett. 67, 1799 (1991).

    Article  ADS  Google Scholar 

  4. A. Hibbs, A. Singsaas, E. Jacobs, A. Bulsara, J. Bekkedahl, F. Moss; J. Appl. Phys. 77, 2582 (1995); R. Rouse, S. Han, J. Lukens; Appl. Phys. Lett. 66, 108 (1995). M. Inchiosa, A. Bulsara, A. Hibbs, B. Whitecotton; Phys. Rev. Lett. 80, 1381 (1998). M. Inchiosa, A. Bulsara, K. Wiesenfeld, L. Gammaitoni; Phys. Lett. A252, 20 (1999).

    Article  ADS  Google Scholar 

  5. R. Mantegna, B. Spagnolo; Phys. Rev. E49, R1792 (1994). I. Liu, J.-M. Liu; Phys. Rev. Lett. 74, 3161 (1995). A. Grigorenko, P. Nikitin, G. Roschchepkin; JETP Lett. 65, 828 (1997). L. Gammaitoni; Phys. Rev. E52, 4691 (1995).

    ADS  Google Scholar 

  6. A. Longtin, A. Bulsara, F. Moss; Phys. Rev. Lett. 67, 656 (1991). J. Douglass, L. Wilkens, E. Pantazelou, F. Moss; Nature 365, 337, (1993). H. Braun, H. Wissing, K. Schafer, M. Hirsch; Nature 367, 270 (1994). J. Levin, J. Miller; Nature 380, 165 (1996). J. Collins, T. Imhoff, P. Grieg; J. Neurophysiol. 76, 642 (1996).

    Article  ADS  Google Scholar 

  7. N. Stocks, N. Stein, S. Soskin, P. McClintock; J. Phys. A25, L1119 (1992). N. Stocks, N. Stein, P. McClintock; J. Phys. A26, L385 (1993).

    ADS  Google Scholar 

  8. L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci; Phys. Rev. Lett. 62, 349 (1989).

    Article  ADS  Google Scholar 

  9. L. Gammaitoni, E. Menichella-Saetta, S. Santucci, F. Marchesoni and C. Presilla; Phys. Rev. A 40, 2114 (1989).

    Article  ADS  Google Scholar 

  10. P. Hänggi, P. Jung, C. Zerbe, and F. Moss; J. Stat. Phys. 70, 25 (1993).

    Article  MATH  ADS  Google Scholar 

  11. I. Kaufman, D. Luchinsky, P. McClintock, S. Soskin, N. Stein, Phys. Lett. A220, 219 (1996).

    ADS  Google Scholar 

  12. M. Grifoni, P. Hänggi; Phys. Rept. 304, 229 (1998).

    Article  ADS  Google Scholar 

  13. P. Hänggi, P. Talkner, M. Borkovec; Rev. Mod. Phys. 62, 251 (1990).

    Article  ADS  Google Scholar 

  14. L. Landau, E. Lifshitz; Mechanics (Pergamon Press, New York 1978)

    Google Scholar 

  15. I. Gradshteyn, I. Ryzhik; Table of Integrals, Series, and Products (Academic Press, New York, 1980).

    MATH  Google Scholar 

  16. R. Stratonovich; Topics in the Theory of Random Noise, Vol. 1, (Gordon and Breach, New York 1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gammaitoni, L., Bulsara, A.R. (2000). Stochastic Resonances in Underdamped Bistable Systems. In: Freund, J.A., Pöschel, T. (eds) Stochastic Processes in Physics, Chemistry, and Biology. Lecture Notes in Physics, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45396-2_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-45396-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41074-4

  • Online ISBN: 978-3-540-45396-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics