The European Physical Journal B

, Volume 58, Issue 3, pp 323–329 | Cite as

Pulse trains propagating through excitable media subjected to external noise

  • V. BeatoEmail author
  • H. Engel
  • L. Schimansky-Geier
Statistical and Nonlinear Physics


We study the propagation of periodic pulse trains in excitable media exposed to external spatio-temporal noise using the light-sensitive Belousov-Zhabotinsky reaction with the underlying Oregonator model as representative example. In the weak noise approximation we find noise-induced transitions in the dispersion relation of pulse trains. We discuss noise-enhanced propagation of pulse trains within a certain wave-length range caused by external noise of moderate strength.


05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 82.40.Bj Oscillations, chaos, and bifurcations 47.54.-r Pattern selection; pattern formation 


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  1. The data presented in this figure, as all the data reported in Figures 1 and 4 and in Section 3, are obtained with the continuation software AUTO. Here the wavelenght is equivalent to the domain size L of the medium in the case of direct numerical simulations under the assumption of periodic boundary conditions Google Scholar
  2. Such a correlation function is obtained numerically by dividing the spatial domain of size L into m cells of equal size l = L/m = nΔx, where Δx is the lattice spacing equal to L/N. In each cell φ fluctuates homogeneously according to φ(x,t)=φ0[1+ηi(t)] for il≤x<(i+1)l, where the stochastic variable ηi is a temporally exponentially correlated stochastic process. The correlation length is in this case \(\lambda=\frac{n}{3}\Delta x\) Google Scholar
  3. S. Alonso, F. Sagués, J.M. Sancho, Phys. Rev. E 65, 066107 (2002) CrossRefADSGoogle Scholar
  4. S. Alonso, I. Sendiña-Nadal, V. Pérez-Muñuzuri, J.M. Sancho, F. Sagués, Phys. Rev. Lett. 87, 078302 (2001) CrossRefADSGoogle Scholar
  5. J. Armero, J. Casademunt, L. Ramírez-Piscina, J.M. Sancho, Phys. Rev. E 58, 5494 (1998) CrossRefADSGoogle Scholar
  6. J. Armero, J.M. Sancho, J. Casademunt, A.M. Lacasta, L. Ramírez-Piscina, F. Sagués, Phys. Rev. Lett. 76, 3045 (1996) CrossRefADSGoogle Scholar
  7. V. Beato, Noise-induced effects in excitable media, Ph.D. thesis, Technische Universität Berlin, 2005 Google Scholar
  8. V. Beato, I. Sendiña-Nadal, I. Gerdes, H. Engel, Phys. Rev. E 71, 035204(R) (2005) CrossRefADSGoogle Scholar
  9. G. Bordiougov, H. Engel, Phys. Rev. Lett. 90, 148302 (2003) CrossRefADSGoogle Scholar
  10. G. Bordiougov, H. Engel, Physica D 215, 25 (2006) zbMATHCrossRefADSGoogle Scholar
  11. H. Brandtstädter, M. Braune, I. Schebesch, H. Engel, Chem. Phys. Lett. 323, 145 (2000) CrossRefGoogle Scholar
  12. O. Carrillo, M.A. Santos, J. Garcia-Ojalvo, J.M. Sancho, Europhys. Lett. 65, 452 (2004) CrossRefADSGoogle Scholar
  13. M. Cross, P. Hohenberg, Rev. Mod. Phys. 65, 851 (1997) CrossRefADSGoogle Scholar
  14. J. Davidenko, A. Pertsov, R. Salomonsz, W. Baxter, J. Jalife, Nature 355, 349 (1992) CrossRefADSGoogle Scholar
  15. E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B. Sandstede, X.-J. Wang, AUTO97: Continuation and bifurcation software for ordinary differential equations. Technical report, Department of Computer Science, Concordia University, Montreal, Canada, 1997, available by FTP from in directory pub/doedel/auto Google Scholar
  16. W. Ebeling, Strukturbildung bei irreversiblen Prozessen (Teubner-Verlag, Leipzig, 1976) Google Scholar
  17. W. Ebeling, H. Herzel, W. Richert, L. Schimansky-Geier, ZAMM 66, 141 (1986) zbMATHCrossRefADSGoogle Scholar
  18. M. Falcke, Adv. Phys. 53, 255 (2004) CrossRefADSGoogle Scholar
  19. M. Falcke, M. Or-Guil, M. Bär, Phys. Rev. Lett. 84, 4753 (2000) CrossRefADSGoogle Scholar
  20. R. Field, R. Noyes, J. Chem. Phys. 60, 1877 (1974) CrossRefGoogle Scholar
  21. J.-M. Flesselles, A. Belmonte, V. Gaspar. J. Chem. Soc., Faraday Trans. 94, 851 (1998) CrossRefGoogle Scholar
  22. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) CrossRefADSGoogle Scholar
  23. J. García-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems (Springer-Verlag, Berlin, 1999) Google Scholar
  24. N. Gorelova, J. Bures, J. Neurobiol 14, 353 (1983) CrossRefGoogle Scholar
  25. C.T. Hamik, N. Manz, O. Steinbock, J. Phys. Chem. 105, 6144 (2001) Google Scholar
  26. S. Jakubith, H.H. Rotermund, W. Engel, A. von Oertzen, G. Ertl, PRL 65, 3013 (1990) CrossRefADSGoogle Scholar
  27. S. Kàdàr, J. Wang, K. Showalter, Nature 391, 770 (1998) CrossRefADSGoogle Scholar
  28. K. Krischer, Nonlinear dynamics in electrochemical systems, edited by R. Alkire, D. Kolb, editors, Adv. Electrochem. Sci. Engr. 8, 89 (2003) Google Scholar
  29. H.J. Krug, L. Pohlmann, L. Kuhnert, J. Phys. Chem. 94, 4862 (1990) CrossRefGoogle Scholar
  30. J. Lechleiter, S. Girard, E. Peralta, D. Clapham, Science 252, 123 (1991) CrossRefADSGoogle Scholar
  31. B. Lindner, J. García-Ojalvo, A. Neiman, L. Schimansky-Geier, Phys. Reports 392, 321 (2004) CrossRefADSGoogle Scholar
  32. E. Meron, Physics Reports 218, 1 (1992) CrossRefADSGoogle Scholar
  33. A.S. Mikhailov, L. Schimansky-Geier, W. Ebeling, Phys. Lett. A96 , 453 (1983) Google Scholar
  34. A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997) zbMATHCrossRefADSGoogle Scholar
  35. X. Sailer, D. Hennig, V. Beato, H. Engel, L. Schimansky-Geier, Phys. Rev. E 73, 056209 (2006) CrossRefADSGoogle Scholar
  36. J.M. Sancho, M.S. Miguel, S.L. Katz, J.D. Gunton, Phys. Rev. A 26, 1589 (1982) CrossRefADSGoogle Scholar
  37. M.A. Santos, J.M. Sancho, Phys. Rev. E 64, 016129 (2001) CrossRefADSGoogle Scholar
  38. M.A. Santos, C.Zülicke, L. Schimansky-Geier, Phys. Lett. A 290, 270 (2001) zbMATHCrossRefADSGoogle Scholar
  39. L. Schimansky-Geier, A.S. Mikhailov, W. Ebeling, Ann. der Phys. 40, 277 (1983) CrossRefADSGoogle Scholar
  40. L. Schimansky-Geier, C. Zülicke, Z. Phys. B 82, 157 (1991) CrossRefGoogle Scholar
  41. I. Sendiña-Nadal, S. Alonso, V. Pérez-Muñuzuri, M.Gómez-Gesteira, V. Peréz-Villar, L. Ramírez-Piscina, J. Casademunt, J.M. Sancho, F. Sagués, Phys. Rev. Lett. 84, 2734 (2000) CrossRefADSGoogle Scholar
  42. F. Siegert, C. Weijer, Proc. Natl. Acad. Sci. USA 89, 6433 (1992) CrossRefADSGoogle Scholar
  43. J. Tyson, P. Fife, J. Chem. Phys. 73, 2224 (1980) CrossRefADSGoogle Scholar
  44. J.J. Tyson, P. Fife, J. Chem. Phys. 73, 2224 (1980) CrossRefADSGoogle Scholar
  45. A. Winfree, Science 175, 634 (1972) CrossRefADSGoogle Scholar
  46. A.T. Winfree, Physica D 49, 125 (1991) CrossRefADSGoogle Scholar
  47. A. Zaikin, A. Zhabotinsky, Nature 225, 535 (1970) CrossRefADSGoogle Scholar
  48. C.Zülicke, A.S. Mikhailov, L. Schimansky Geier, Physica A 163, 559 (1990) CrossRefADSGoogle Scholar

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© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Technische Universität Berlin, Institut für Theoretische PhysikBerlinGermany
  2. 2.Università “La Sapienza” di RomaRomaItaly
  3. 3.Humboldt-Universität zu Berlin, Institut für PhysikBerlinGermany

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