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The European Physical Journal B

, Volume 60, Issue 4, pp 507–513 | Cite as

Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing

  • F. N. Si
  • Q. X. LiuEmail author
  • J. Z. Zhang
  • L. Q. Zhou
Statistical and Nonlinear Physics

Abstract.

It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. 88, 138301 (2002)]. As a further investigation, here we observe different types of traveling waves under different noises and periodic forces, using a simplified Oregonator model. Depending on different noises and periodic forces, we have observed different types of wave propagation (or their disappearance). Moreover, reversal phenomena are observed in this system based on the numerical experiments in the one-dimensional space. We explain this as an effect of periodic forces. Thus, we give qualitative explanations for how stable reversal phenomena appear, which seem to arise from the mixing function of the periodic force and the noise. The output period and three velocities (normal, positive and negative) of the travelling waves are defined and their relationship with the periodic forces, along with the types of waves, are also studied in sub-excitable system under a fixed noise intensity.

PACS.

82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer 05.40.Ca Noise 47.54.-r Pattern selection; pattern formation 83.60.Np Effects of electric and magnetic fields 

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References

  1. W. Horsthemke, R. Lefever, Noise-Induced Transi-tions: Theory and Applications in Physics, Chemistry and Biology (Springer-Verlag, Berlin, 1984) Google Scholar
  2. R. Mankin, T. Laas, A. Sauga, A. Ainsaar, E. Reiter, Phys. Rev. E 74, 021101 (2006) CrossRefADSMathSciNetGoogle Scholar
  3. S. Aumaître, K. Mallick, F. Pétrélis, J. Stat. Mech. 2007, P07016 (2007) Google Scholar
  4. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) CrossRefADSGoogle Scholar
  5. H. Zhonghuai, Y. Lingfa, X. Zuo, X. Houwen, Phys. Rev. Lett. 81, 2854 (1998) CrossRefGoogle Scholar
  6. K. Wiesenteld, F. Moss, Nature (London) 373, 33 (1995) CrossRefADSGoogle Scholar
  7. P. Jung, G. Mayer-Kress, Phys. Rev. Lett. 74, 2130 (1995) CrossRefADSGoogle Scholar
  8. J.F. Lindner, S. Chandramouli, A.R. Bulsara, M. Löcher, W.L. Ditto, Phys. Rev. Lett. 81, 5048 (1998) CrossRefADSGoogle Scholar
  9. F. Marchesoni, L. Gammaitoni, A.R. Bulsara, Phys. Rev. Lett. 76, 2609 (1996) CrossRefADSGoogle Scholar
  10. M. Marchi, F. Marchesoni, L. Gammaitoni, E. Menichella-Saetta, S. Santucci, Phys. Rev. E 54, 3479 (1996) CrossRefADSGoogle Scholar
  11. T. Leiber, F. Marchesoni, H. Risken, Phys. Rev. A 38, 983 (1988) CrossRefADSMathSciNetGoogle Scholar
  12. M. Feingold, D.L. Gonzalez, O. Piro, H. Viturro, Phys. Rev. A 37, 4060 (1988) CrossRefADSGoogle Scholar
  13. E. Meron, Phys. Rep. 218, 1 (1992) CrossRefADSMathSciNetGoogle Scholar
  14. A.S. Mikhailov, Foundations of Synergetics I: Distributed Active Systems (Springer, New York, 1990) Google Scholar
  15. S. Kádár, J. Wang, K. Showalter, Nature 391, 770 (1998) CrossRefADSGoogle Scholar
  16. J. Wang, S. Kádár, P. Jung, K. Showalter, Phys. Rev. Lett. 82, 855 (1999) CrossRefADSGoogle Scholar
  17. H. Hempel, L. Schimansky-Geier, J. García-Ojalvo, Phys. Rev. Lett. 82, 3713 (1999) CrossRefADSGoogle Scholar
  18. A.N. Zakin, A.M. Zhabotinsky, Nature 225, 535 (1970) CrossRefADSGoogle Scholar
  19. R.J. Field, E. Koros, R.M. Noyes, J. Am. Chem. Soc. 94, 8649 (1972) CrossRefGoogle Scholar
  20. L.Q. Zhou, X. Jia, Q. Ouyang, Phys. Rev. Lett. 88, 138301 (2002) CrossRefADSGoogle Scholar
  21. S. Alonso, I. Sendiña-Nadal, V. Pérez-Muñuzuri, J.M. Sancho, F. Sagués, Phys. Rev. Lett. 87, 078302 (2001) CrossRefADSGoogle Scholar
  22. J. Garcia-Ojalvo, J.M. Sancho, Noise in spatially extended systems (Springer, New York, 1999) Google Scholar
  23. D.S. Dean, I.T. Drummond, R.R. Horgan, J. Stat. Mech. 2007, P07013 (2007) Google Scholar
  24. V. Krinsky, E. Hamm, V. Voignier, Phys. Rev. Lett. 76, 3854 (1996) CrossRefADSGoogle Scholar
  25. Z. Neufeld, I.Z. Kiss, C. Zhou, J. Kurths, Phys. Rev. Lett. 91, 084101 (2003) CrossRefADSGoogle Scholar
  26. Z. Neufeld, C. López, E. Hernández-García, O. Piro, Phys. Rev. E 66, 066208 (2002) CrossRefADSMathSciNetGoogle Scholar
  27. C. Zhou, J. Kurths, New J. Phys. 7, 18 (2005) CrossRefGoogle Scholar
  28. C. Zhou, J. Kurths, Z. Neufeld, I.Z. Kiss, Phys. Rev. Lett. 91, 150601 (2003) CrossRefADSGoogle Scholar
  29. J.J. Tyson, P.C. Fife, J. Chem. Phys. 73, 2224 (1980) CrossRefADSMathSciNetGoogle Scholar
  30. R.A. Albanese, in Inverse Problems in Wave Propagation, edited by G. Chavent, G. Papanicolaou, P. Sacks, W. Symes (Springer-Verlag, 1997) Google Scholar
  31. W. Jahnke, A.T. Winfree, Inter. J. Bifur. Chaos 1, 445 (1991) zbMATHCrossRefMathSciNetGoogle Scholar
  32. D. Higham, SIAM Rev. 43, (2001) Google Scholar
  33. W. Jahnke, W.E. Skaggs, A.T. Winfree, J. Phys. Chem. 93, 740 (1989) CrossRefGoogle Scholar
  34. A.T. Winfree, W. Jahnke, J. Phys. Chem. 93, 2823 (1989) CrossRefGoogle Scholar
  35. J.J. Tyson, Oscillations and traveling waves in chemical systems (Wiley, N.Y., 1985) Google Scholar
  36. F. Sagués, J.M. Sancho, J. Garcia-Ojalvo, Rev. Mode. Phys. 79, 829 (2007) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Authors and Affiliations

  • F. N. Si
    • 1
    • 2
  • Q. X. Liu
    • 3
    Email author
  • J. Z. Zhang
    • 2
    • 4
  • L. Q. Zhou
    • 2
  1. 1.China Academy of Engineering PhysicsSichuanP.R. China
  2. 2.Department of PhysicsPeking UniversityBeijingP.R. China
  3. 3.Department of MathematicsNorth University of ChinaShan'xiP.R. China
  4. 4.Department of PhysicsNortheastern UniversityBostonUSA

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