Skip to main content
SpringerLink
Log in

Symmetry breakdown of stochastic potential by noise cross-correlations among colored noise sources

  • Regular Article
  • Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

A nontrivial phenomenon in stochastic zero-dimensional systems, namely, the symmetry breakdown of stationary probability function due to the correlation between the noises is studied. As a model system to study this effect, we consider a generalized synergetic system of Lorenz type with Gaussian colored noise of each mode. In the frameworks of theoretical approximation and numerical simulations it is shown the fluctuation cross-correlations break the symmetry of bistable synergetic potential, producing an asymmetric effective potential. At that, cross-correlations play the twofold role: cross-correlations are the reason of symmetry breaking at small cross-correlation times on the one hand, and the reason of symmetry restoring at large values of cross-correlation times on the other hand. Moreover, it is shown that symmetry breakdown occurs only if one of multiplicative function is odd. Any other combinations of noises restore the symmetric form of potential.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. Horsthemke, R. Lefever, Noise-Induced Transitions (Springer-Verlag, Berlin, 1984)

  2. Noise in Nonlinear Dynamical Systems, edited by F. Moss, P.V.E. McClintock (Cambridge University Press, Cambridge, 1989)

  3. P. Luque, J. García-Ojalvo, J.M. Sancho, in Fluctuation Phenomena: Disorder and Nonlinearity, edited by A.R. Bishop, S. Jiménez, L. Váquez (World Scientific, Singapore, 1995)

  4. S. Mangioni, R. Deza, H.S. Wio, R. Toral, Phys. Rev. Lett. 79, 2389 (1997)

    Article  ADS  Google Scholar 

  5. S.E. Mangioni, R.R. Deza, R. Toral, H.S. Wio, Phys. Rev. E 61, 223 (2000)

    Article  ADS  Google Scholar 

  6. P. Pechukas, P. Hänggi, Phys. Rev. Lett. 73, 2772 (1994)

    Article  ADS  Google Scholar 

  7. Ch.R. Doering, J.C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992)

    Article  ADS  Google Scholar 

  8. P. Hänggi, P. Jung, Adv. Chem. Phys. 89, 239 (1995)

    Article  Google Scholar 

  9. S. Kai, S. Wakabayashi, M. Imasaki, Phys. Rev. A 33, 2612 (1986)

    Article  ADS  Google Scholar 

  10. S. Zhu, A.W. Yu, R. Roy, Phys. Rev. A 34, 4333 (1986)

    Article  ADS  Google Scholar 

  11. A.A. Zaikin, J. Kurths, Chaos 11, 570 (2001)

    Article  ADS  MATH  Google Scholar 

  12. K.P. Singh, G. Ropars, M. Brunel, A. Le Floch, Phys. Rev. Lett. 90, 073901 (2003)

    Article  ADS  Google Scholar 

  13. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)

    Article  ADS  Google Scholar 

  14. C.J. Tessone, H.S. Wio, P. Hänggi, Phys. Rev. E 62, 4623 (2000)

    Article  ADS  Google Scholar 

  15. P. Hänggi, ChemPhysChem 3, 285 (2002)

    Article  Google Scholar 

  16. Y. Jia, J.-R. Li, Phys. Rev. Lett. 78, 994 (1997)

    Article  ADS  Google Scholar 

  17. L. Cao, D.-J. Wu, Phys. Lett. A 260, 126 (1999)

    Article  ADS  Google Scholar 

  18. R.D. Astumian, P. Hänggi, Phys. Today 55, 33 (2002)

    Article  Google Scholar 

  19. P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  20. A.J.R. Madureira, P. Hänggi, H.S. Wio, Phys. Lett. A 217, 248 (1996)

    Article  ADS  Google Scholar 

  21. H.-X. Fu, L. Cao, D.-J. Wu, Phys. Rev. E 59, R6235 (1999)

    Article  ADS  Google Scholar 

  22. S.I. Denisov, A.N. Vitrenko, W. Horsthemke, Phys. Rev. E 68, 046132 (2003)

    Article  ADS  Google Scholar 

  23. M. Mierzejewski, J. Dajka, J. Luczka, P. Talkner, P. Hänggi, Phys. Rev. E 74, 041102 (2006)

    Article  ADS  Google Scholar 

  24. Y. Jia, J.R. Li, Physica A 252, 417 (1998)

    Article  Google Scholar 

  25. LI Dong-Xi, XU Wei, WANG Liang, XU Yong, Commun. Theor. Phys. 50, 396 (2008)

    Article  ADS  Google Scholar 

  26. P. Hänggi, T.T. Mroczkowski, F. Moss, P.V.E. McClintock, Phys. Rev. A 32, 695 (1985)

    Article  ADS  Google Scholar 

  27. R.F. Fox, R. Roy, Phys. Rev. A 35, 1838 (1987)

    Article  ADS  Google Scholar 

  28. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992)

  29. H. Dekker, Phys. Lett. A 90, 26 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  30. V.E. Shapiro, Phys. Rev. E 48, 109 (1993)

    Article  ADS  Google Scholar 

  31. D.O. Kharchenko, I.A. Knyaz', Eur. Phys. J. B 32, 375 (2003)

    Article  ADS  Google Scholar 

  32. A.I. Olemskoi, D.O. Kharchenko, I.A. Knyaz', Phys. Rev. E 71, 041101 (2005)

    Article  ADS  Google Scholar 

  33. P. Hänggi, Z. Phys. B 31, 407 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  34. P. Jung, P. Hänggi, Phys. Rev. A 35, 4464 (1987)

    Article  ADS  Google Scholar 

  35. L. Hwalisz, P. Jung, P. Hänggi, P. Talkner, L. Schimansky-Geier, Z. Phys. B 77, 471 (1989)

    Article  ADS  Google Scholar 

  36. P. Hänggi, Chem. Phys. 180, 157 (1994)

    Article  ADS  Google Scholar 

  37. P. Hänggi, in Stochastic Processes Applied to Physics, edited by L. Pesquera, M. Rodriguez (World Scientific, Singapore and Philadelphia, 1985), pp. 69–95

  38. H. Haken, Synergetics, An Introduction (Springer-Verlag, Berlin, 1983)

  39. G. Nicolis, I. Prigogine, Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations (JohnWiley, New York, 1977)

  40. A.I. Olemskoi, I. Krackovský, Physica A 291, 79 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  41. H. Risken, The Fokker-Plank equation (Springer-Verlag, Berlin, 1989)

  42. L. Ramírez-Piscina, J.M. Sancho, F.J. de la Rubia, K. Lindenberg, G.P. Tsironis, Phys. Rev. A 40, 2120 (1989)

    Article  ADS  Google Scholar 

  43. F. Drolet, J. Viñals, Phys. Rev. E 57, 5036 (1998)

    Article  ADS  Google Scholar 

  44. A.I. Olemskoi, A.V. Khomenko, Zh. Eksp. Teor. Fiz. 83, 1180 (1996)

    Google Scholar 

  45. E.A. Novikov, Sov. Phys. JETP 20, 1290 (1965)

    Google Scholar 

  46. A.I. Olemskoi, Usp. Fiz. Nauk 168, 287 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Modeling of Complex Systems Dept., Sumy State University, 2, R. Korsakova Str., 40007, Sumy, Ukraine

    I. A. Knyaz’

Authors
  1. I. A. Knyaz’
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Knyaz’.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knyaz’, I.A. Symmetry breakdown of stochastic potential by noise cross-correlations among colored noise sources. Eur. Phys. J. B 83, 235 (2011). https://doi.org/10.1140/epjb/e2011-20525-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2011-20525-y

Keywords

Search

Navigation