Advertisement

Olami-Feder-Christensen model on different networks

  • F. CarusoEmail author
  • V. Latora
  • A. Pluchino
  • A. Rapisarda
  • B. Tadić
Networks

Abstract.

We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality. Indeed, in this case we observe power law behavior of earthquakes size distribution with finite size scaling for the cut-off region. In the scale-free OFC model, instead, the strength of disorder hinders synchronization and does not allow to reach a critical state.

PACS.

05.65.+b Self-organized systems 45.70.Ht Avalanches 89.75.Da Systems obeying scaling laws 91.30.Bi Seismic sources (mechanisms, magnitude, moment frequency spectrum)  

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, 1987) Google Scholar
  2. P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A. 38, 364 (1988) CrossRefADSMathSciNetGoogle Scholar
  3. P. Bak, How Nature Works: The Science of Self-Organized Criticality (Copernicus, New York, 1996) Google Scholar
  4. H. Jensen, Self-Organized Criticality (Cambridge Univ. Press, New York, 1998) Google Scholar
  5. Z. Olami, H.J.S. Feder, K. Christensen, Phys. Rev. Lett. 68, 1244 (1992); K. Christensen, Z. Olami, Phys. Rev. A 46, 1829 (1992) CrossRefADSGoogle Scholar
  6. W. Klein, J. Rundle, Phys. Rev. Lett. 71, 1288 (1993); K. Christensen, Phys. Rev. Lett. 71, 1289 (1993) CrossRefADSGoogle Scholar
  7. J.X. Carvalho, C.P.C. Prado, Phys. Rev. Lett. 84, 4006 (2000) CrossRefADSGoogle Scholar
  8. K. Christensen, D. Hamon, H.J. Jensen, S. Lise, Phys. Rev. Lett. 87, 039801 (2001); J.X. Carvalho, C.P.C. Prado, Phys. Rev. Lett. 87, 039802 (2001) CrossRefADSGoogle Scholar
  9. S. Lise, M. Paczuski, Phys. Rev. E, 63, 036111 (2001) Google Scholar
  10. S. Lise, M. Paczuski, Phys. Rev. Lett. 88, 228301 (2002) CrossRefADSGoogle Scholar
  11. F. Caruso, V. Latora, A. Rapisarda, B. Tadic, in Proceedings of 31st Workshop of the International School of Solid State Physics: Complexity, Metastability and Nonextensivity, Erice, Italy, edited by C. Beck, G. Benedek, A. Rapisarda, C. Tsallis, The Science and Culture Series Physics (World Scientific, 2005), pp. 355-360 Google Scholar
  12. S. Abe, N. Suzuki, Europhys. Lett. 65, 581 (2004) and reference therein CrossRefADSGoogle Scholar
  13. S. Abe, N. Suzuki, J. Geophys. Res. [Solid Earth] 108 (B2), 2113 (2003) CrossRefADSGoogle Scholar
  14. J. Davidsen, M. Paczuski, Phys. Rev. Lett. 94, 048501 (2005) and reference therein CrossRefADSGoogle Scholar
  15. A.L. Barabási, R. Albert, Science 286, 509 (1999) CrossRefMathSciNetGoogle Scholar
  16. S. Lise, M. Paczuski, Phys. Rev. E 64, 046111 (2001) CrossRefADSGoogle Scholar
  17. S. Lise, H.J. Jensen, Phys. Rev. Lett. 76, 2326 (1996) CrossRefADSGoogle Scholar
  18. M.L. Chabanol, V. Hakim, Phys. Rev. E 56, 2343 (1997) CrossRefADSGoogle Scholar
  19. H.M. Broker, P. Grassberger, Phys. Rev. E 56, 3944 (1997) CrossRefADSGoogle Scholar
  20. O. Kinouchi, S.T.R. Pinho, C.P.C. Prado, Phys. Rev. E 58, 3997 (1998) CrossRefADSGoogle Scholar
  21. A.A. Middleton, C. Tang, Phys. Rev. Lett. 74, 742 (1995) CrossRefADSGoogle Scholar
  22. J.E.S. Socolar, G. Grinstein, C. Jayaprakash, Phys. Rev. E 47, 2366 (1993) CrossRefADSGoogle Scholar
  23. P. Grassberger, Phys. Rev. E 49, 2436 (1994) CrossRefADSGoogle Scholar
  24. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998) CrossRefADSGoogle Scholar
  25. More in general in Watts and Strogatz original definition a small-world network is characterized not only by a small value of L, but also by an high clustering coefficient Google Scholar
  26. R.S. Stein, Nature 402, 605 (1999) CrossRefADSGoogle Scholar
  27. P. Tosi, V. De Rubeis, V. Loreto, L. Pietronero, Ann. Geophys. 47, 1849 (2004) Google Scholar
  28. Y.Y. Kagan, D.D. Jackson, Geophys. J. Int. 104, 117 (1991) Google Scholar
  29. D.P. Hill et al., Science 260, 1617 (1993) Google Scholar
  30. L. Crescentini, A. Amoruso, R. Scarpa, Science 286, 2132 (1999) CrossRefGoogle Scholar
  31. T. Parsons, J. Geophys. Res. 107, 2199 (2001) CrossRefGoogle Scholar
  32. M.S. Mega, P. Allegrini, P. Grigolini, V. Latora, L. Palatella, A. Rapisarda, S. Vinciguerra, Phys. Rev. Lett. 90, 188501 (2003); F. Caruso, S. Vinciguerra, V. Latora, A. Rapisarda, S. Malone, physics/0311049, Fractals (2006), in press CrossRefADSGoogle Scholar
  33. K.-I. Goh, D.-S. Lee, B. Kahng, D. Kim, Phys. Rev. Lett. 91, 148701 (2003) CrossRefADSGoogle Scholar
  34. D.J. Watts, Small Worlds (Princeton Univ. Press, Princeton, New Jersey, 1999) Google Scholar
  35. H. Ceva, Phys. Rev. E 52, 154 (1995) CrossRefADSGoogle Scholar
  36. M. Mousseau, Phys. Rev. Lett. 77, 968 (1996) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • F. Caruso
    • 1
    Email author
  • V. Latora
    • 2
  • A. Pluchino
    • 2
  • A. Rapisarda
    • 2
  • B. Tadić
    • 3
  1. 1.Scuola Superiore di Catania, via S. Paolo 73CataniaItaly
  2. 2.Dipartimento di Fisica e AstronomiaUniversità di CataniaCataniaItaly
  3. 3.Department for Theoretical PhysicsJožef Stefan InstituteLjubljanaSlovenia

Personalised recommendations