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Cascading toppling dynamics on scale-free networks

Author

Listed:
  • Goh, K.-I.
  • Lee, D.-S.
  • Kahng, B.
  • Kim, D.

Abstract

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd(k)∼k-γ, through the Bak–Tang–Wiesenfeld sandpile model. The threshold height of a node i is set to be ki1-η with 0⩽η<1. We obtain the exponents for the avalanche size and the duration distributions analytically as a function of γ and η by using the branching process approach. The analytic solution is checked with numerical simulations on both artificial uncorrelated networks such as the static model and real-world networks. While numerical results of the avalanche size distribution for artificial uncorrelated scale-free networks are in reasonable agreement with the analytic prediction, those for real-world networks are not, which may be attributed to non-trivial degree–degree correlations in real-world networks.

Suggested Citation

  • Goh, K.-I. & Lee, D.-S. & Kahng, B. & Kim, D., 2005. "Cascading toppling dynamics on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 93-103.
    • Handle: RePEc:eee:phsmap:v:346:y:2005:i:1:p:93-103
    DOI: 10.1016/j.physa.2004.08.054
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    Cited by:

    1. Nicky Zachariou & Paul Expert & Misako Takayasu & Kim Christensen, 2015. "Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-13, November.

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