Journal of Statistical Physics

, Volume 101, Issue 1–2, pp 473–481 | Cite as

Excitable Structures in Stochastic Bistable Media

  • J. García-Ojalvo
  • L. Schimansky-Geier
Article

Abstract

We examine the influence of parametric noise on the spatiotemporal behavior of a bistable medium with activator–inhibitor dynamics. Deterministic front propagation in one dimension is seen to be destabilized by the external noise, resulting in the propagation of solitary pulses through the system. For large enough noise levels, this state becomes unstable via a backfiring mechanism, which eventually leads to a turbulent state.

reaction diffusion system noise-induced phenomena activator–inhibitor dynamics pulse propagation 

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REFERENCES

  1. 1.
    C. Nicolis and G. Nicolis, Tellus 33:225 (1981); R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 14:L453 (1981); C. Nicolis, Tellus 34:1 (1982); R. Benzi, A. Sutera, G. Parisi, and A. Vulpiani, Tellus 34:10 (1982).Google Scholar
  2. 2.
    F. Moss, in Contemporary Problems in Statistical Physics, G. H. Weiss, ed. (SIAM, Philadelphia, 1994), p. 205.Google Scholar
  3. 3.
    L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70:223 (1998).Google Scholar
  4. 4.
    V. S. Anishchenko, A. B. Neiman, F. Moss, and L. Schirnansky-Geier, Sov. Phys. Usp. 42:7 (1999).Google Scholar
  5. 5.
    M. Misono, T. Kohmoto, Y. Fukuda, and M. Kunimoto, Phys. Rev. E 58:5602 (1998).Google Scholar
  6. 6.
    A. Neiman, A. Silchenko, V. Anishchenko, and L. Schimansky-Geier, Phys. Rev. E 58:7118 (1998).Google Scholar
  7. 7.
    J. García-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999).Google Scholar
  8. 8.
    L. Schimansky-Geier and Ch. Zülicke, Z. Phys. B 82:157 (1991).Google Scholar
  9. 9.
    J. Armero, J. M. Sancho, J. Casademunt, A. M. Lacasta, L. Ramírez-Piscina, and F. Sagués, Phys. Rev. Lett. 76:3045 (1996).Google Scholar
  10. 10.
    J. García-Ojalvo and L. Schimansky-Geier, Europhys. Lett. 47:298 (1999).Google Scholar
  11. 11.
    F. Baras, Phys. Rev. Lett. 77:1398 (1996).Google Scholar
  12. 12.
    P. Jung and G. Mayer-Kress, Chaos 5:458 (1995); P. Jung and G. Mayer-Kress, Phys. Rev. Lett. 74:2130 (1995).Google Scholar
  13. 13.
    S. Kadar, J. Wang, and K. Showalter, Nature (London) 391:770 (1998); F. Moss, Nature (London) 391:743 (1998)Google Scholar
  14. 14.
    H. Hempel, L. Schimansky-Geier, and J. García-Ojalvo, Phys. Rev. Lett. 82:3713 (1999); A. Neiman, L. Schimansky-Geier, A. Cornell-Bell, and F. Moss, Phys. Rev. Lett. 83:4896 (1999).Google Scholar
  15. 15.
    P. Jung, A. Cornell-Bell, K. Madden, and F. Moss, J. Neurophysiol. 79:1098 (1998); P. Jung, A. Cornell-Bell, F. Moss, S. Kadar, J. Wang, and K. Showalter, Chaos 8:567 (1998).Google Scholar
  16. 16.
    M. Lücher, D. Cigna, and E. R. Hunt, Phys. Rev. Lett. 80:5212 (1998).Google Scholar
  17. 17.
    Y. Zhang, G. Hu, and L. Gammaitoni, Phys. Rev. E 58:2952 (1998).Google Scholar
  18. 18.
    J. F. Lindner, S. Chandramouli, A. R. Bulsara, M. Löcher, and W. L. Ditto, Phys. Rev. Lett. 81:5048 (1998).Google Scholar
  19. 19.
    C. Nicolis, G. Nicolis, and H. L. Frisch, Phys. Lett A 249:443 (1998).Google Scholar
  20. 20.
    J. García-Ojalvo, A. M. Lacasta, J. M. Sancho, and R. Toral, Europhys. Lett. 42:125 (1998).Google Scholar
  21. 21.
    M. Ibañes, J. García-Ojalvo, R. Toral, and J. M. Sancho, Phys. Rev. E 60:3597 (1999).Google Scholar
  22. 22.
    G. Nicolis and I. Progogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).Google Scholar
  23. 23.
    A. Mikhailov, Foundations of Synergetics I, 2nd edn. (Springer, Berlin, 1994).Google Scholar
  24. 24.
    J. D. Murray, Mathematical Biology (Springer, Berlin, 1989).Google Scholar
  25. 25.
    D. Barkley, M. Kness, and L. S. Tuckerman, Phys. Rev. A 42:2489 (1990).Google Scholar
  26. 26.
    D. Barkley, Physica D 49:61 (1991).Google Scholar
  27. 28.
    M. Bär, M. Hildebrand, M. Eiswirth, M. Falcke, H. Engel, and M. Neufeld, Chaos 4:499 (1994).Google Scholar
  28. 29.
    M. G. Zimmermann, S. O. Firle, M. A. Natiello, M. Hildebrand, M. Eiswirth, M. Bär, A. K. Bangia, and I. G. Kevrekidis, Physica D 110:92 (1997).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • J. García-Ojalvo
    • 1
    • 2
  • L. Schimansky-Geier
    • 1
  1. 1.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Departament de Física i Enginyeria NuclearUniversitat Politècnica de CatalunyaTerrassaSpain

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