Stochastic resonance: influence of a f noise spectrum

  • M. A. FuentesEmail author
  • H. S. Wio
Statistical and Nonlinear Physics


With the aim of studying stochastic resonance (SR) in a double-well potential when the noise source has a spectral density of the form f (with varying κ), we have extended a procedure introduced by Kaulakys et al. (Phys. Rev. E 70, 020101 (2004)). In order to achieve an analytical understanding of the results, we have obtained an effective Markovian approximation that allows us to make a systematic study of the effect of such noise on the SR phenomenon. A comparison of the numerical and analytical results shows an excellent qualitative agreement indicating that the effective Markovian approximation is able to correctly describe the general trends.


02.50.Ey Stochastic processes 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 02.50.-r Probability theory, stochastic processes, and statistics  


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) CrossRefADSGoogle Scholar
  2. T. Wellens, V. Shatokhin, A. Buchleitner, Rep. Prog. Phys. 67, 45 (2004) CrossRefADSGoogle Scholar
  3. M.A. Fuentes, R. Toral, H.S. Wio, Physica A 295, 114 (2001); F.J. Castro, M.N. Kuperman, M.A. Fuentes, H.S. Wio, Phys. Rev. E 64, 051105 (2001); M.A. Fuentes, H.S. Wio, R. Toral, Physica A 303, 91 (2002); M.A. Fuentes, C. Tessone, H.S. Wio, R. Toral, Fluct. Noise Letters 3, 365 (2003) zbMATHCrossRefADSGoogle Scholar
  4. See for instance: Unsolved Problems of Noise: Proc. Conf. UPoN'96, edited by Ch. Doering, L.B. Kiss, M. Shlesinger (World Scientific, Singapore, 1997); Fractals and Beyond, edited by M. Novak (World Scientific, Singapore, 1998); Noise in Complex Systems and Stochastic Dynamics, edited by L. Schimansky-Geier, D. Abbott, A. Neiman, C. Van den Broeck, Proc. SPIE 5114 (2003); COMPLEXUS MUNDI: Emergent Patterns in Nature, edited by M. Novak (World Scientific, Singapore, 2005) Google Scholar
  5. P. Makra, Z. Gingl, T. Fülei, Phys. Lett. A 317, 228 (2003) zbMATHCrossRefADSGoogle Scholar
  6. I. Hidaka, D. Nozaki, Y. Yamamoto, Phys. Rev. Lett. 85, 3740 (2000) CrossRefADSGoogle Scholar
  7. R. Soma, D. Nozaki, S. Kwak, Y. Yamamoto, Phys. Rev. Lett. 91, 078101 (2003) CrossRefADSGoogle Scholar
  8. P. Ruszczynski, L. Kish, Phys. Lett. A 276, 187 (2000) MathSciNetCrossRefADSGoogle Scholar
  9. D. Nozaki, S. Kwak, Y. Yamamoto, Phys. Lett. A 243, 281 (1998) CrossRefADSGoogle Scholar
  10. D. Nozaki, D.J. Mar, P. Grieg, J.J. Collins, Phys. Rev. Lett. 82, 2402 (1999) CrossRefADSGoogle Scholar
  11. D. Nozaki, J.J. Collins, Y. Yamamoto, Phys. Rev. E 60, 4637 (1999) CrossRefADSGoogle Scholar
  12. B. Kaulakys, J. Ruseckas, Phys. Rev. E 70, 020101 (2004) CrossRefADSGoogle Scholar
  13. B. Kaulakys, V. Gontis, M. Alaburda, Phys. Rev. E 71, 051105 (2005) MathSciNetCrossRefADSGoogle Scholar
  14. B. Kaulakys, J. Ruseckas, V. Gontis, M. Alaburda, e-print arXiv:cond-mat/0509626 (2005) Google Scholar
  15. P. Jung, P. Hänggi, Phys. Rev. A 35, 4464 (1987); L. H'walisz, P. Jung, P. Hänggi, P. Talkner, L. Schimansky-Geier, Z. Physik B 77, 471 (1989) CrossRefADSGoogle Scholar
  16. H.S. Wio, P. Colet, L. Pesquera, M.A. Rodriguez, M. San Miguel, Phys. Rev. A 40, 7312 (1989); P. Hänggi, Chem. Phys. 180, 157 (1994), F. Castro, A. Sánchez, H.S. Wio, Phys. Rev. Lett. 75, 1691 (1995); S. Mangioni, R. Deza, H.S. Wio, R. Toral, Phys. Rev. Lett. 79, 2389 (1997) MathSciNetCrossRefADSGoogle Scholar
  17. C.W. Gardiner, Handbook of Stochastic Methods, 2nd edn. (Springer-Verlag, Berlin, 1985) Google Scholar
  18. S. Bouzat, H.S. Wio, Phys. Rev. E 59, 5142 (1999) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.Centro Atómico Bariloche and Instituto BalseiroRío NegroArgentina
  2. 2.Santa Fe InstituteSanta FeUSA
  3. 3.Instituto de Fisica de Cantabria, Universidad de Cantabria and CSICSantanderSpain

Personalised recommendations