Critical behavior of a stochastic anisotropic Bak–Sneppen model

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Abstract

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak–Sneppen (saBS) model, in which a parameter α is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness fc and the critical exponent τr by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    B. Gutenberg, C. Richter, Ann. Geofits 9, 1 (1956) Google Scholar
  2. 2.
    S. Gould, N. Eldredge, Paleobiology 3, 114 (1977) Google Scholar
  3. 3.
    I. Bose, I. Chaudhuri, Int. J. Mod. Phys. C 12, 675 (2001) ADSCrossRefGoogle Scholar
  4. 4.
    P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987) ADSCrossRefGoogle Scholar
  5. 5.
    P. Bak, M. Paczuski, Proc. Natl. Acad. Sci. 92, 6689 (1995) ADSCrossRefGoogle Scholar
  6. 6.
    R. Dickman, A.M. Miguel, A. Vespignani, S. Zapperi, Braz. J. Phys. 30, 27 (2000) ADSCrossRefGoogle Scholar
  7. 7.
    R. Dickman, A. Vespignani, S. Zapperi, Phys. Rev. E 57, 5095 (1998) ADSCrossRefGoogle Scholar
  8. 8.
    P. Bak, K. Sneppen, Phys. Rev. Lett. 71, 4083 (1993) ADSCrossRefGoogle Scholar
  9. 9.
    K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992) ADSCrossRefGoogle Scholar
  10. 10.
    S. Zaitsev, Phys. A: Stat. Mech. Appl. 189, 411 (1992) CrossRefGoogle Scholar
  11. 11.
    D. Wilkinson, J.F. Willemsen, J. Phys. A: Math. Gen. 16, 3365 (1983) ADSCrossRefGoogle Scholar
  12. 12.
    L.H. Tang, H. Leschhorn, Phys. Rev. A 45, R8309 (1992) ADSCrossRefGoogle Scholar
  13. 13.
    H. Leschhorn, L.H. Tang, Phys. Rev. E 49, 1238 (1994) ADSCrossRefGoogle Scholar
  14. 14.
    L.H. Tang, H. Leschhorn, Phys. Rev. Lett. 70, 3832 (1993) ADSCrossRefGoogle Scholar
  15. 15.
    P. Grassberger, Phys. Lett. A 200, 277 (1995) ADSCrossRefGoogle Scholar
  16. 16.
    M. Paczuski, S. Maslov, P. Bak, Phys. Rev. E 53, 414 (1996) ADSCrossRefGoogle Scholar
  17. 17.
    S.N. Dorogovtsev, J.F.F. Mendes, Y.G. Pogorelov, Phys. Rev. E 62, 295 (2000) ADSCrossRefGoogle Scholar
  18. 18.
    S. Boettcher, M. Paczuski, Phys. Rev. Lett. 84, 2267 (2000) ADSCrossRefGoogle Scholar
  19. 19.
    P. De Los Rios, M. Marsili, M. Vendruscolo, Phys. Rev. Lett. 80, 5746 (1998) ADSCrossRefGoogle Scholar
  20. 20.
    P. Grassberger, Phys. Lett. A 200, 277 (1995) ADSCrossRefGoogle Scholar
  21. 21.
    G.J. Garcia, R. Dickman, Phys. A: Stat. Mech. Appl. 342, 164 (2004) CrossRefGoogle Scholar
  22. 22.
    S. Maslov, Phys. Rev. Lett. 77, 1182 (1996) ADSCrossRefGoogle Scholar
  23. 23.
    D. Stauffer, M.E.J. Newman, Int. J. Mod. Phys. C 12, 1375 (2001) ADSCrossRefGoogle Scholar
  24. 24.
    H. Flyvbjerg, K. Sneppen, P. Bak, Phys. Rev. Lett. 71, 4087 (1993) ADSCrossRefGoogle Scholar
  25. 25.
    M. Marsili, P. De Los Rios, S. Maslov, Phys. Rev. Lett. 80, 1457 (1998) ADSCrossRefGoogle Scholar
  26. 26.
    S. Maslov, P. De Los Rios, M. Marsili, Y.C. Zhang, Phys. Rev. E 58, 7141 (1998) ADSCrossRefGoogle Scholar
  27. 27.
    S.S. Manna, Phys. Rev. E 80, 021132 (2009) ADSCrossRefMathSciNetGoogle Scholar
  28. 28.
    L. Wei, C. Xu, Chin. Phys. Lett. 19, 1420 (2002) ADSCrossRefGoogle Scholar
  29. 29.
    W. Li, Y. Luo, Y. Wang, A. Cai, Chin. Sci. Bull. 56, 3639 (2011) CrossRefGoogle Scholar
  30. 30.
    R. Cafiero, P. De Los Rios, A. Valleriani, J.L. Vega, Phys. Rev. E 60, R1111 (1999) ADSCrossRefGoogle Scholar
  31. 31.
    M. Vergeles, Phys. Rev. Lett. 75, 1969 (1995) ADSCrossRefGoogle Scholar
  32. 32.
    R. Cafiero, P. De Los Rios, F.M. Dittes, A. Valleriani, J.L. Vega, Phys. Rev. E 58, 3993 (1998) ADSCrossRefGoogle Scholar
  33. 33.
    G.J. Garcia, R. Dickman, Phys. A: Stat. Mech. Appl. 342, 516 (2004) CrossRefGoogle Scholar
  34. 34.
    M. Grinfeld, P.A. Knight, A.R. Wade, Phys. Rev. E 84, 041124 (2011) ADSCrossRefGoogle Scholar
  35. 35.
    W. Li, X. Cai, Phys. Rev. E 61, 771 (2000) ADSCrossRefGoogle Scholar
  36. 36.
    W. Li, X. Cai, Phys. Rev. E 61, 5630 (2000) ADSCrossRefGoogle Scholar
  37. 37.
    W. Li, X. Cai, Phys. Rev. E 62, 7743 (2000) ADSCrossRefGoogle Scholar
  38. 38.
    U. Tirnakli, M.L. Lyra, Int. J. Mod. Phys. C 14, 805 (2003) ADSCrossRefGoogle Scholar
  39. 39.
    B. Bakar, U. Tirnakli, Phys. A: Stat. Mech. Appl. 387, 5110 (2008) CrossRefGoogle Scholar
  40. 40.
    U. Tirnakli, M.L. Lyra, Phys. A: Stat. Mech. Appl. 342, 151 (2004) CrossRefGoogle Scholar
  41. 41.
    K. Christensen, R. Donangelo, B. Koiller, K. Sneppen, Phys. Rev. Lett. 81, 2380 (1998) ADSCrossRefGoogle Scholar
  42. 42.
    T. Gross, B. Blasius, J. R. Soc. Interface 5, 259 (2008) CrossRefGoogle Scholar
  43. 43.
    D. Garlaschelli, A. Capocci, G. Caldarelli, Nat. Phys. 3, 813 (2007) CrossRefGoogle Scholar
  44. 44.
    G. Caldarelli, A. Capocci, D. Garlaschelli, Eur. Phys. J. B 64, 585 (2008) ADSCrossRefGoogle Scholar
  45. 45.
    M. Paczuski, D. Hughes, Phys. A: Stat. Mech. Appl. 342, 158 (2004) CrossRefGoogle Scholar
  46. 46.
    R.V. Kulkarni, E. Almaas, D. Stroud (1999), arXiv:cond-mat/9905066 [cond-mat.stat-mech]
  47. 47.
    Y. Moreno, A. Vazquez, Europhys. Lett. 57, 765 (2002) ADSCrossRefGoogle Scholar
  48. 48.
    S.M. Bhattacharjee, F. Seno, J. Phys. A: Math. Gen. 34, 6375 (2001) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Computer and Communication Engineering, Zhengzhou University of Light IndustryZhengzhouP.R. China
  2. 2.Complexity Science Center, Central China Normal UniversityWuhanP.R. China
  3. 3.National Engineering Laboratory for Technology of Big Data Applications in Education, Central China Normal UniversityWuhanP.R. China

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