Advertisement

Stochastic resonance driven by time-delayed feedback in a bistable system with colored noise

Regular Article

Abstract

The phenomenon of stochastic resonance (SR) driven by time-delayed feedback in a bistable system with colored noise is investigated. Combining the small time delay and unified colored noise approximation, the Fokker-Planck equation is obtained. The different effects of time delay and noise correlation time on stationary probability density and signal-to-noise ratio (SNR) are discussed respectively. It is found that time delay can markedly improve the output SNR. This method can be practically applied to many fields such as weak signal extraction, recovery and so on. Numerical simulations are presented and are in agreement with the approximate theoretical results.

Keywords

Nonlinear Dynamics 

References

  1. 1.
    R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A 14, L453 (1981) MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    B. McNamara, K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989) ADSCrossRefGoogle Scholar
  3. 3.
    P. Jungand, P. Hanggi, Phys. Rev. A 44, 8032 (1991) ADSCrossRefGoogle Scholar
  4. 4.
    G. Hu, T. Ditzinger, C.Z. Ning, H. Haken, Phys. Rev. Lett. 71, 807 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    L. Gamma, F. Marchesoni, S. Santucci, Phys. Rev. Lett. 74, 1052 (1995) ADSCrossRefGoogle Scholar
  6. 6.
    P. Jung, G. Maye-Kress, Phys. Rev. Lett. 74, 2130 (1995) ADSCrossRefGoogle Scholar
  7. 7.
    W. Yang, M. Ding, G. Hu, Phys. Rev. Lett. 74, 3955 (1995) ADSCrossRefGoogle Scholar
  8. 8.
    G. Hu, H. Haken, F. Xie, Phys. Rev. Lett. 77, 1925 (1996) CrossRefGoogle Scholar
  9. 9.
    J.M.G. Vilar, J.M. Rubi, Phys. Rev. Lett. 78, 2882 (1997) ADSCrossRefGoogle Scholar
  10. 10.
    J.M.G. Vilar, J.M. Rubi, Phys. Rev. Lett. 78, 2886 (1997) ADSCrossRefGoogle Scholar
  11. 11.
    J.M.G. Vilar, G. Gomula, J.M. Rubi, Phys. Rev. Lett. 81, 14 (1998)ADSCrossRefGoogle Scholar
  12. 12.
    L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 224 (1998)ADSCrossRefGoogle Scholar
  13. 13.
    M.K.S. Yeung, S.H. Strogatz, Phys. Rev. Lett. 82, 648 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    S. Kim, S.H. Park, H.B. Pyo, Phys. Rev. Lett. 82, 1620 (1999) ADSCrossRefGoogle Scholar
  15. 15.
    T. Ohira, Y. Sato, Phys. Rev. Lett. 82, 2811 (1999) ADSCrossRefGoogle Scholar
  16. 16.
    A.A. Zaikin, J. Kurths, L. Schimansky-Geier, Phys. Rev. Lett. 85, 227 (2000)ADSCrossRefGoogle Scholar
  17. 17.
    Y. Jia, S. Yu, J. Li, Phys. Rev. E 62, 1869 (2000) ADSCrossRefGoogle Scholar
  18. 18.
    H. Haken, Eur. Phys. J. B 18, 545 (2000)ADSCrossRefGoogle Scholar
  19. 19.
    A.A. Zaikin, K. Murali, J. Kurths, Phys. Rev. E 63, 020103 (2001) ADSCrossRefGoogle Scholar
  20. 20.
    H.E. Plesser, T. Geisel, Phys. Rev. E 63, 031916 (2001) ADSCrossRefGoogle Scholar
  21. 21.
    N.G. Stocks, Phys. Rev. E 63, 041114 (2001) ADSCrossRefGoogle Scholar
  22. 22.
    R. Rozenfeld, J.A. Freund, A. Neiman, L. Schimansky- Geier, Phys. Rev. E 64, 051107 (2001) ADSCrossRefGoogle Scholar
  23. 23.
    X. Luo, S. Zhu, Phys. Rev. E 67, 021104 (2003) ADSCrossRefGoogle Scholar
  24. 24.
    N.B. Janson, A.G. Balanov, E. Scholl, Phys. Rev. Lett. 93, 010601 (2004) ADSCrossRefGoogle Scholar
  25. 25.
    L. Gammaitoni, M. Locher, A. Bulsara, P. Hanggi, J. Neff, K. Wiesenfeld, W.L. Ditto, M.E. Inchiosa, Phys. Rev. Lett. 82, 4574 (1999) ADSCrossRefGoogle Scholar
  26. 26.
    J. Mason, J.F. Lindner, J. Neff, W.L. Ditto, A.R. Bulsara, M.L. Spano, Phys. Lett. A 277, 13 (2000)ADSCrossRefGoogle Scholar
  27. 27.
    N. Baba, A. Amann, E. Scholl, W. Just, Phys. Rev. Lett. 89, 074101 (2002) ADSCrossRefGoogle Scholar
  28. 28.
    D. Goldobin, M. Rosenblum, A. Pikovsky, Phys. Rev. E 67, 061119 (2003) ADSCrossRefGoogle Scholar
  29. 29.
    H. Hasegawa, Phys. Rev. E 70, 021911 (2004) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    M.-Y. Kim, R. Roy, J.L. Aron, T.W. Carr, I.B. Schwartz, Phys. Rev. Lett. 94, 088101 (2005) ADSCrossRefGoogle Scholar
  31. 31.
    T. Piwonski, J. Houlihan, T. Busch, G. Huyet, Phys. Rev. Lett. 95, 040601 (2005) ADSCrossRefGoogle Scholar
  32. 32.
    Y. Chembo Kouomou, P. Colet, L. Larger, N. Gastaud, Phys. Rev. Lett. 95, 203903 (2005) ADSCrossRefGoogle Scholar
  33. 33.
    Dan Wu, Shiqun Zhu, Phys. Rev. E 73, 051107 (2006) ADSCrossRefGoogle Scholar
  34. 34.
    M.A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. Lopez-Amo, K. Panajotov, Phys. Rev. Lett. 99, 023903 (2007) ADSCrossRefGoogle Scholar
  35. 35.
    A. Passian, A.L. Lereu, D. Yi, S. Barhen, T. Thundat, Phys. Rev. B 75, 233403 (2007) ADSCrossRefGoogle Scholar
  36. 36.
    M. Borromeo, F. Marchesoni, Phys. Rev. E 75, 041106 (2007) ADSCrossRefGoogle Scholar
  37. 37.
    S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 59, 3970 (1999) ADSCrossRefGoogle Scholar
  38. 38.
    S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 61, 4906 (2000) ADSCrossRefGoogle Scholar
  39. 39.
    X. Gu, S. Zhu, D. Wu, Eur. Phys. J. D 42, 461 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    X. Gu, S. Zhu, Eur. Phys. J. D 56, 215 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    Zhang HuiQing, Xu Wei, Xu Yong, Zhou BingChang, Science 53, 745 (2010)Google Scholar
  42. 42.
    M.C. Mackey, I.G. Nechaeva, Phys. Rev. E 52, 6681 (1995) MathSciNetCrossRefGoogle Scholar
  43. 43.
    K. Patanarapeelert, T.D. Frank, R. Friedrich, P.J. Beek, I.M. Tang, Phys. Lett. A 360, 190 (2006) ADSMATHCrossRefGoogle Scholar
  44. 44.
    M. Gong, F. Guo, J. Stat. Phys. 142, 386 (2011) MathSciNetADSMATHCrossRefGoogle Scholar
  45. 45.
    C.W. Eurich, J.G. Milton, Phys. Rev. E 54, 6681 (1996) ADSCrossRefGoogle Scholar
  46. 46.
    Y. Chen, M. Ding, J.A. Scott Kelso, Phys. Rev. Lett. 79, 4501 (1997) ADSCrossRefGoogle Scholar
  47. 47.
    T. Ohira, T. Yamane, Phys. Rev. E 61, 1247 (2000) ADSCrossRefGoogle Scholar
  48. 48.
    R.J. Peterka, Biol. Cybern. 82, 335 (2000)CrossRefGoogle Scholar
  49. 49.
    L.S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001) ADSCrossRefGoogle Scholar
  50. 50.
    C. Masoller, Phys. Rev. Lett. 88, 034102 (2002) ADSCrossRefGoogle Scholar
  51. 51.
    J.L. Cabrera, J.G. Milton, Phys. Rev. Lett. 89, 158702 (2002) ADSCrossRefGoogle Scholar
  52. 52.
    C. Masoller, Phys. Rev. Lett. 90, 020601 (2003) ADSCrossRefGoogle Scholar
  53. 53.
    J. Houlihan, D. Goulding, Th. Busch, C. Masoller, G. Huyet, Phys. Rev. Lett. 92, 050601 (2004) ADSCrossRefGoogle Scholar
  54. 54.
    A.A. Budini, M.O. Caceres, Phys. Rev. E 70, 046104 (2004) ADSCrossRefGoogle Scholar
  55. 55.
    P. Jung, P. Hanggi, Phys. Rev. A 35, 4464 (1987) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Suzhou UniversityJiangsuP.R. China
  2. 2.Nanjing Institute of Railway TechnologyJiangsuP.R. China

Personalised recommendations