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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 f c and the critical exponent τ r 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.

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References

  1. B. Gutenberg, C. Richter, Ann. Geofits 9, 1 (1956)

    Google Scholar 

  2. S. Gould, N. Eldredge, Paleobiology 3, 114 (1977)

    Google Scholar 

  3. I. Bose, I. Chaudhuri, Int. J. Mod. Phys. C 12, 675 (2001)

    Article  ADS  Google Scholar 

  4. P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)

    Article  ADS  Google Scholar 

  5. P. Bak, M. Paczuski, Proc. Natl. Acad. Sci. 92, 6689 (1995)

    Article  ADS  Google Scholar 

  6. R. Dickman, A.M. Miguel, A. Vespignani, S. Zapperi, Braz. J. Phys. 30, 27 (2000)

    Article  ADS  Google Scholar 

  7. R. Dickman, A. Vespignani, S. Zapperi, Phys. Rev. E 57, 5095 (1998)

    Article  ADS  Google Scholar 

  8. P. Bak, K. Sneppen, Phys. Rev. Lett. 71, 4083 (1993)

    Article  ADS  Google Scholar 

  9. K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992)

    Article  ADS  Google Scholar 

  10. S. Zaitsev, Phys. A: Stat. Mech. Appl. 189, 411 (1992)

    Article  Google Scholar 

  11. D. Wilkinson, J.F. Willemsen, J. Phys. A: Math. Gen. 16, 3365 (1983)

    Article  ADS  Google Scholar 

  12. L.H. Tang, H. Leschhorn, Phys. Rev. A 45, R8309 (1992)

    Article  ADS  Google Scholar 

  13. H. Leschhorn, L.H. Tang, Phys. Rev. E 49, 1238 (1994)

    Article  ADS  Google Scholar 

  14. L.H. Tang, H. Leschhorn, Phys. Rev. Lett. 70, 3832 (1993)

    Article  ADS  Google Scholar 

  15. P. Grassberger, Phys. Lett. A 200, 277 (1995)

    Article  ADS  Google Scholar 

  16. M. Paczuski, S. Maslov, P. Bak, Phys. Rev. E 53, 414 (1996)

    Article  ADS  Google Scholar 

  17. S.N. Dorogovtsev, J.F.F. Mendes, Y.G. Pogorelov, Phys. Rev. E 62, 295 (2000)

    Article  ADS  Google Scholar 

  18. S. Boettcher, M. Paczuski, Phys. Rev. Lett. 84, 2267 (2000)

    Article  ADS  Google Scholar 

  19. P. De Los Rios, M. Marsili, M. Vendruscolo, Phys. Rev. Lett. 80, 5746 (1998)

    Article  ADS  Google Scholar 

  20. P. Grassberger, Phys. Lett. A 200, 277 (1995)

    Article  ADS  Google Scholar 

  21. G.J. Garcia, R. Dickman, Phys. A: Stat. Mech. Appl. 342, 164 (2004)

    Article  Google Scholar 

  22. S. Maslov, Phys. Rev. Lett. 77, 1182 (1996)

    Article  ADS  Google Scholar 

  23. D. Stauffer, M.E.J. Newman, Int. J. Mod. Phys. C 12, 1375 (2001)

    Article  ADS  Google Scholar 

  24. H. Flyvbjerg, K. Sneppen, P. Bak, Phys. Rev. Lett. 71, 4087 (1993)

    Article  ADS  Google Scholar 

  25. M. Marsili, P. De Los Rios, S. Maslov, Phys. Rev. Lett. 80, 1457 (1998)

    Article  ADS  Google Scholar 

  26. S. Maslov, P. De Los Rios, M. Marsili, Y.C. Zhang, Phys. Rev. E 58, 7141 (1998)

    Article  ADS  Google Scholar 

  27. S.S. Manna, Phys. Rev. E 80, 021132 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  28. L. Wei, C. Xu, Chin. Phys. Lett. 19, 1420 (2002)

    Article  ADS  Google Scholar 

  29. W. Li, Y. Luo, Y. Wang, A. Cai, Chin. Sci. Bull. 56, 3639 (2011)

    Article  Google Scholar 

  30. R. Cafiero, P. De Los Rios, A. Valleriani, J.L. Vega, Phys. Rev. E 60, R1111 (1999)

    Article  ADS  Google Scholar 

  31. M. Vergeles, Phys. Rev. Lett. 75, 1969 (1995)

    Article  ADS  Google Scholar 

  32. R. Cafiero, P. De Los Rios, F.M. Dittes, A. Valleriani, J.L. Vega, Phys. Rev. E 58, 3993 (1998)

    Article  ADS  Google Scholar 

  33. G.J. Garcia, R. Dickman, Phys. A: Stat. Mech. Appl. 342, 516 (2004)

    Article  Google Scholar 

  34. M. Grinfeld, P.A. Knight, A.R. Wade, Phys. Rev. E 84, 041124 (2011)

    Article  ADS  Google Scholar 

  35. W. Li, X. Cai, Phys. Rev. E 61, 771 (2000)

    Article  ADS  Google Scholar 

  36. W. Li, X. Cai, Phys. Rev. E 61, 5630 (2000)

    Article  ADS  Google Scholar 

  37. W. Li, X. Cai, Phys. Rev. E 62, 7743 (2000)

    Article  ADS  Google Scholar 

  38. U. Tirnakli, M.L. Lyra, Int. J. Mod. Phys. C 14, 805 (2003)

    Article  ADS  Google Scholar 

  39. B. Bakar, U. Tirnakli, Phys. A: Stat. Mech. Appl. 387, 5110 (2008)

    Article  Google Scholar 

  40. U. Tirnakli, M.L. Lyra, Phys. A: Stat. Mech. Appl. 342, 151 (2004)

    Article  Google Scholar 

  41. K. Christensen, R. Donangelo, B. Koiller, K. Sneppen, Phys. Rev. Lett. 81, 2380 (1998)

    Article  ADS  Google Scholar 

  42. T. Gross, B. Blasius, J. R. Soc. Interface 5, 259 (2008)

    Article  Google Scholar 

  43. D. Garlaschelli, A. Capocci, G. Caldarelli, Nat. Phys. 3, 813 (2007)

    Article  Google Scholar 

  44. G. Caldarelli, A. Capocci, D. Garlaschelli, Eur. Phys. J. B 64, 585 (2008)

    Article  ADS  Google Scholar 

  45. M. Paczuski, D. Hughes, Phys. A: Stat. Mech. Appl. 342, 158 (2004)

    Article  Google Scholar 

  46. R.V. Kulkarni, E. Almaas, D. Stroud (1999), arXiv:cond-mat/9905066 [cond-mat.stat-mech]

  47. Y. Moreno, A. Vazquez, Europhys. Lett. 57, 765 (2002)

    Article  ADS  Google Scholar 

  48. S.M. Bhattacharjee, F. Seno, J. Phys. A: Math. Gen. 34, 6375 (2001)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Computer and Communication Engineering, Zhengzhou University of Light Industry, Zhengzhou, P.R. China

    Jihui Han

  2. Complexity Science Center, Central China Normal University, Wuhan, P.R. China

    Wei Li & Webing Deng

  3. National Engineering Laboratory for Technology of Big Data Applications in Education, Central China Normal University, Wuhan, P.R. China

    Zhu Su

Authors
  1. Jihui Han
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  2. Wei Li
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  3. Zhu Su
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  4. Webing Deng
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Correspondence to Jihui Han or Wei Li.

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Han, J., Li, W., Su, Z. et al. Critical behavior of a stochastic anisotropic Bak–Sneppen model. Eur. Phys. J. B 90, 220 (2017). https://doi.org/10.1140/epjb/e2017-80022-y

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  • DOI: https://doi.org/10.1140/epjb/e2017-80022-y

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