Advertisement

Journal of the Korean Physical Society

, Volume 60, Issue 4, pp 641–647 | Cite as

Sandpiles on multiplex networks

  • Kyu-Min Lee
  • K. -I. Goh
  • I. -M. Kim
Article

Abstract

We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche dynamics; the system is critical with an asymptotic power-law avalanche size distribution with an exponent τ = 3/2 on duplex random networks. The detailed cascade dynamics, however, is affected by the multiplex coupling. For example, higher-degree nodes such as hubs in scale-free networks fail more often in the multiplex dynamics than in the simplex network counterpart in which different types of edges are simply aggregated. Our results suggest that multiplex modeling would be necessary in order to gain a better understanding of cascading failure phenomena of real-world multiplex complex systems, such as the global economic crisis.

Keywords

Multiplex networks Sandpiles Cascading failure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. E. J. Newman, A.-L. Barabási and D. J. Watts, The Structure and Dynamics of Networks (Princeton University Press, Princeton, 2006).zbMATHGoogle Scholar
  2. [2]
    R. Cohen and S. Havlin, Complex Networks: Structure, Robustness and Function (Cambridge University Press, Cambridge, 2010).zbMATHGoogle Scholar
  3. [3]
    A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).zbMATHCrossRefGoogle Scholar
  4. [4]
    M. L. Sachtjen, B. A. Carreras and V. E. Lynch, Phys. Rev. E 61, 4877 (2000).ADSCrossRefGoogle Scholar
  5. [5]
    A. E. Motter and Y.-C. Lai, Phys. Rev. E 66, 065102 (2002).ADSCrossRefGoogle Scholar
  6. [6]
    E. J. Lee, K.-I. Goh, B. Kahng and D. Kim, Phys. Rev. E 71, 056108 (2005).ADSCrossRefGoogle Scholar
  7. [7]
    K.-M. Lee, J.-S. Yang, G. Kim, J. Lee, K.-I. Goh and I.-M. Kim, PLoS ONE 6, e18443 (2011).ADSCrossRefGoogle Scholar
  8. [8]
    P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988).MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    D. J. Watts, Proc. Natl. Acad. Sci. U.S.A. 99, 5766 (2002)MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10]
    S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley and S. Havlin, Nature 464, 1025 (2010).ADSCrossRefGoogle Scholar
  11. [11]
    E. A. Leicht and R. M. D’souza, arXiv:0907.0894.Google Scholar
  12. [12]
    M. Szell, R. Lambiotte and S. Thurner, Proc. Natl. Acad. Sci. U.S.A. 107, 13636 (2010).ADSCrossRefGoogle Scholar
  13. [13]
    K.-M. Lee, J. Y. Kim, W.-k. Cho, K.-I. Goh and I.-M. Kim, arXiv:1111.0107.Google Scholar
  14. [14]
    H. J. Jensen, Self-organized Criticality (Cambridge University Press, Cambridge, 1998).zbMATHGoogle Scholar
  15. [15]
    P. Alstrøm, Phys. Rev. A 38, 4905 (1988).ADSCrossRefGoogle Scholar
  16. [16]
    E. Bonabeau, J. Phys. Soc. Jpn. 64, 327 (1995)ADSCrossRefGoogle Scholar
  17. [17]
    K.-I. Goh, D.-S. Lee, B. Kahng and D. Kim, Phys. Rev. Lett. 91, 148701 (2003).ADSCrossRefGoogle Scholar
  18. [18]
    D.-S. Lee, K.-I. Goh, B. Kahng and D. Kim, J. Korean Phys. Soc. 44, 633 (2004).ADSCrossRefGoogle Scholar
  19. [19]
    D.-S. Lee, K.-I. Goh, B. Kahng and D. Kim, Physica A 338, 84 (2004).ADSCrossRefGoogle Scholar
  20. [20]
    K.-I. Goh, D.-S. Lee, B. Kahng and D. Kim, Physica A 346, 93 (2005).ADSCrossRefGoogle Scholar
  21. [21]
    J. Um, P. Minnhagen and B. J. Kim, Chaos 21, 025106 (2011).MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    C. D. Brummitt, K.-M. Lee and K.-I. Goh, arXiv: 1112.0093.Google Scholar
  23. [23]
    P. Erdős and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).Google Scholar
  24. [24]
    C. D. Brummitt, R. M. D’souza and E. A. Leicht, arXiv:1106.4499v1.Google Scholar
  25. [25]
    K.-I. Goh, B. Kahng and D. Kim, Phys. Rev. Lett. 87, 278701 (2001).ADSCrossRefGoogle Scholar
  26. [26]
    P. Grassberger and S. S. Manna, J. Phys. 51, 1077 (1990).CrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2012

Authors and Affiliations

  1. 1.Department of Physics and Institute of Basic ScienceKorea UniversitySeoulKorea

Personalised recommendations