Generalized Nagumo model: interesting effects of parameters’ fluctuations

Regular Article

Abstract

In this paper, we used an analytical method to calculate the effects that produce the parameter’s fluctuations characterizing a generalization of Nagumo model. (The extinction option is replaced by one of low density homogeneous population.) Moreover, we also check the results by means of numerical simulations of the corresponding stochastic process. We find that these fluctuations have a strong impact on the solutions producing interesting changes.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    W. Horsthemke, R. Lefever, Noise Induced Transitions (Springer, Berlin, 1984)Google Scholar
  2. 2.
    L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)CrossRefADSGoogle Scholar
  3. 3.
    J. García-Ojalvo, J.M. Sancho, Noise in Spatially Extended System (Springer-Verlag, New York, 1999)Google Scholar
  4. 4.
    C. Van den Broeck, J.M.R. Parrondo, R. Toral, Phys. Rev. Lett. 73, 3395 (1994)CrossRefADSGoogle Scholar
  5. 5.
    C. Van den Broeck, J.M.R. Parrondo, R. Toral, R. Kawai, Phys. Rev. E 55, 4084 (1997)CrossRefADSGoogle Scholar
  6. 6.
    S. Mangioni, R. Deza, H.S. Wio, R. Toral, Phys. Rev. Lett. 79, 2389 (1997)CrossRefADSGoogle Scholar
  7. 7.
    S. Mangioni, R. Deza, R. Toral, H.S. Wio, Phys. Rev. E 61, 223 (2000)CrossRefADSGoogle Scholar
  8. 8.
    S.E. Mangioni, R. Deza, H.S. Wio, Phys. Rev. E 63, 041115 (2001)CrossRefADSGoogle Scholar
  9. 9.
    P. Reimann, Phys. Rep. 361, 57 (2002)MATHMathSciNetCrossRefADSGoogle Scholar
  10. 10.
    M. Ibañes, J. García-Ojalvo, R. Toral, J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001)CrossRefADSGoogle Scholar
  11. 11.
    O. Carrillo, M. Ibañes, J. García-Ojalvo, J. Casademunt, J.M. Sancho, Phys. Rev. E 67, 046110 (2003)CrossRefADSGoogle Scholar
  12. 12.
    J. Buceta, M. Ibañes, J.M. Sancho, K. Lindenberg, Phys. Rev. E 67, 021113 (2003)CrossRefADSGoogle Scholar
  13. 13.
    J. Buceta, K. Lindenberg, Phys. Rev. E 69, 011102 (2004)MathSciNetCrossRefADSGoogle Scholar
  14. 14.
    K. Wood, J. Buceta, K. Lindenberg, Phys. Rev. E 73, 022101 (2006)CrossRefADSGoogle Scholar
  15. 15.
    J. Dunkel, W. Ebeling, L. Schimansky-Geier, P. Hänggi, Phys. Rev. E 67, 061118 (2003)CrossRefADSGoogle Scholar
  16. 16.
    J. Dunkel, W. Ebeling, L. Schimansky-Geier, P. Hänggi, Phys. Rev. E 69, 056118 (2004)MathSciNetCrossRefADSGoogle Scholar
  17. 17.
    F. Sagués, J.M. Sancho, J. García-Ojalvo, Rev. Mod. Phys. 79, 829 (2007)CrossRefADSGoogle Scholar
  18. 18.
    R. Toral, C.J. Tessone, J. Viana Lopez, Eur. Phys. J. Special Topics 143, 59 (2007)CrossRefADSGoogle Scholar
  19. 19.
    P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)CrossRefADSGoogle Scholar
  20. 20.
    S.E. Mangioni, H.S. Wio, Phys. Rev. E 71, 056203 (2005)CrossRefADSGoogle Scholar
  21. 21.
    S.E. Mangioni, Physica A 389, 1799 (2010)CrossRefADSGoogle Scholar
  22. 22.
    S.E. Mangioni, R. Deza, Phys. Rev. E 82, 042101 (2010)CrossRefADSGoogle Scholar
  23. 23.
    S.E. Mangioni, R.R. Deza, Physica A 391, 4191 (2012)CrossRefADSGoogle Scholar
  24. 24.
    S.E. Mangioni, R.R. Deza, paper submitted for publication (Phys. Rev. E)Google Scholar
  25. 25.
    S.E. Mangioni, Eur. Phys. J. B 88, 53 (2015)MathSciNetCrossRefADSGoogle Scholar
  26. 26.
    J.D. Murray, Mathematical Biology, 2nd edn. (Springer, New York, 1993)Google Scholar
  27. 27.
    R. FitzHugh, Bull. Math. Biophys. 17, 257278 (1955)CrossRefGoogle Scholar
  28. 28.
    R. FitzHugh, Biophys. J. 1, 445466 (1961)Google Scholar
  29. 29.
    R. FitzHugh, Mathematical models of excitation and propagation in nerve, in Biological Engineering, edited by H.P. Schwan (McGrawHill Book Co., New York, 1969), Chap. 1, p. 185Google Scholar
  30. 30.
    J. Nagumo, S. Arimoto, S. Yoshizawa, Proc. IRE. 50, 2061 (1962)CrossRefGoogle Scholar
  31. 31.
    S.E. Mangioni, Eur. Phys. J. B 87, 248 (2014)MathSciNetCrossRefADSGoogle Scholar
  32. 32.
    P. Hänggi, K.E. Shuler, I. Oppenheim, Physica A 107, 143 (1981)MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    P. Hänggi, H. Grabert, P. Talkner, H. Thomas, Phys. Rev. A 29, 371 (1984)MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    J.A. Kromer, L. Schimansky-Geier, R. Toral, Phys. Rev. E 87, 063311 (2013)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.IFIMAR (Universidad Nacional de Mar del Plata and CONICET)Mar del PlataArgentina

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