The European Physical Journal B

, Volume 65, Issue 3, pp 443–451 | Cite as

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

Article

Abstract

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal response. Finally we show that the self-correlation of the colored noise causes a reduction of the effective noise intensity, which appears as a rescaling of the fluctuations affecting the FHN system.

PACS

87.19.ll Models of single neurons and networks 87.19.lc Noise in the nervous system 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 05.45.-a Nonlinear dynamics and chaos 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    See the special section on “Complex Systems”, Science 284, 79 (1999); O.N. Bjornstad, B.T. Grenfell, Science 293, 638 (2001); S. Ciuchi, F. de Pasquale, B. Spagnolo, Phys. Rev. E 53, 706 (1996); M. Scheffer, S.R. Carpenter, J.A. Foley, C. Folke, B. Walker, Nature 413, 591 (2001); B. Spagnolo, D. Valenti, A. Fiasconaro, Math. Biosc. Engineering 1, 185 (2004)CrossRefGoogle Scholar
  2. 2.
    C.R. Doering, J.C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992); R.N. Mantegna, B. Spagnolo, Phys. Rev. Lett. 84, 3025 (2000); P. Majee, G. Goswami, B. Chandra Bag, Chem. Phys. Lett. 416, 256 (2005); R. Gommers, P. Douglas, S. Bergamini, M. Goonasekera, P.H. Jones, F. Renzoni, Phys. Rev. Lett. 94, 143001 (2005)CrossRefADSGoogle Scholar
  3. 3.
    R.N. Mantegna, B. Spagnolo, Phys. Rev. Lett. 76, 563 (1996); R. Wackerbauer, Phys. Rev. E 59, 2872 (1999); A. Mielke, Phys. Rev. Lett. 84, 818 (2000); B. Spagnolo, A.A. Dubkov, N.V. Agudov, Acta Phys. Pol. 35, 1419 (2004); G. Bonanno, D. Valenti, B. Spagnolo, Phys. Rev E 75, 016106 (2007)CrossRefADSGoogle Scholar
  4. 4.
    N.V. Agudov, B. Spagnolo, Phys. Rev. E 64, 035102 (2001); A.A. Dubkov, N.V. Agudov, B. Spagnolo, Phys. Rev. E 69, 061103 (2004)CrossRefADSGoogle Scholar
  5. 5.
    E. Lanzara, R.N. Mantegna, B. Spagnolo, R. Zangara, Am. J. Phys. 65, 341 (1997); L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998); Y. Kashimori, H. Funakubo, T. Kambara, Biophys. J. 75, 1700 (1998); D. Valenti, A. Fiasconaro, B. Spagnolo, Phys. A 331, 477 (2004); B. Kosko, S. Mitaim, Phys. Rev. E 70, 031911 (2004); A. Caruso, M.E. Gargano, D. Valenti, A. Fiasconaro, B. Spagnolo, Fluc. Noise Lett. 5, L349 (2005)CrossRefADSGoogle Scholar
  6. 6.
    K. Wiesenfeld, F. Moss, Nature 373, 33 (1995); F. Chapeau-Blondeau, X. Godivier, N. Chambet, Phys. Rev. E 53, 1273 (1996); Special Issue: Advances in neural networks research IJCNN’03, B. Kosko, S. Mitaim, Neural Networks 16, 755 (2003)CrossRefADSGoogle Scholar
  7. 7.
    A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952); E.V. Pankratova, A.V. Polovinkin, E. Mosekilde, Eur. Phys. J. B 45, 391 (2005); V.N. Belykh, E.V. Pankratova, Int. J. Bifurcation Chaos 18, (2008) in press.Google Scholar
  8. 8.
    K.F. Bonhoeffer, J. Gen. Physiol. 32, 69 (1948); K.F. Bonhoeffer, Naturwissenschaften 40, 301 (1953)CrossRefGoogle Scholar
  9. 9.
    B. van der Pol, J. van der Mark, Arch. Néerl. Physiol. 14, 418 (1929)Google Scholar
  10. 10.
    R. FitzHugh, Bull. Math. Biophysics 17, 257 (1955); R. FitzHugh, J. Gen. Physiol. 43, 867 (1960); R. FitzHugh, Biophys. J. 1, 445 (1961)CrossRefGoogle Scholar
  11. 11.
    J.H. Hale, H. Kocak, Dynamics and Bifurcations (Springer-Verlag, New York, 1991)MATHGoogle Scholar
  12. 12.
    C. Rocsoreanu, A. Georgescu, N. Giurgiteanu, The FitzHugh-Nagumo Model: Bifurcation and Dynamics (Kluwer Academic Publishers, Boston, 2000)MATHGoogle Scholar
  13. 13.
    J. Nagumo, S. Arimoto, S. Yoshizawa, Proc. IRE 50, 2061 (1964)CrossRefGoogle Scholar
  14. 14.
    J. Keener, J. Sneyd, Mathematical Physiology (Springer-Verlag, New York, 1998)MATHGoogle Scholar
  15. 15.
    X. Pei, K. Bachmann, F. Moss, Phys. Lett. A 206, 61 (1995)CrossRefADSGoogle Scholar
  16. 16.
    A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997)MATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    D. Nozaki, Y. Yamamoto, Phys. Lett. A 243, 281 (1998)CrossRefADSGoogle Scholar
  18. 18.
    A. Longtin, D.R. Chialvo, Phys. Rev. Lett. 81, 4012 (1998)CrossRefADSGoogle Scholar
  19. 19.
    E.V. Pankratova, A.V. Polovinkin, B. Spagnolo, Phys. Lett. A 344, 43 (2005)MATHCrossRefADSGoogle Scholar
  20. 20.
    C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin, 1993)Google Scholar
  21. 21.
    D. Valenti, A. Fiasconaro, B. Spagnolo, Mod. Prob. Stat. Phys. 2, 91 (2003); D. Valenti, A. Fiasconaro, B. Spagnolo, Fluc. Noise Lett. 5, L337 (2005); D. Valenti, L. Schimansky-Geier, X. Sailer, B. Spagnolo, M. Iacomi, A. Phys. Pol. B 38, 1961 (2007)Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Dipartimento di Fisica e Tecnologie Relative, Group of Interdisciplinary PhysicsUniversità di Palermo and CNISM-INFM, Unità di PalermoViale delle ScienzeItaly

Personalised recommendations