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Sandpile avalanche dynamics on scale-free networks

Author

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

Abstract

Avalanche dynamics is an indispensable feature of complex systems. Here, we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent γ through the Bak–Tang–Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as ki1−η with 0⩽η<1, where ki is the degree of node i. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents τ and δ, respectively. They are given as τ=(γ−2η)/(γ−1−η) and δ=(γ−1−η)/(γ−2) for γ<3−η, 3/2 and 2 for γ>3−η, respectively. The power-law distributions are modified by a logarithmic correction at γ=3−η.

Suggested Citation

  • Lee, D.-S. & Goh, K.-I. & Kahng, B. & Kim, D., 2004. "Sandpile avalanche dynamics on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 84-91.
  • Handle: RePEc:eee:phsmap:v:338:y:2004:i:1:p:84-91
    DOI: 10.1016/j.physa.2004.02.028
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    Cited by:

    1. Aggarwal, Sandeep Kumar & Pastén, Denisse & Khan, Prosanta Kumar, 2017. "Multifractal analysis of 2001 Mw7.7 Bhuj earthquake sequence in Gujarat, Western India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 177-186.
    2. Jian Zhou & Weijian Zheng & Dali Wang & David W. Coit, 2024. "A resilient network recovery framework against cascading failures with deep graph learning," Journal of Risk and Reliability, , vol. 238(1), pages 193-203, February.
    3. Pastén, Denisse & Pavez-Orrego, Claudia, 2023. "Multifractal time evolution for intraplate earthquakes recorded in southern Norway during 1980–2021," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Lahtinen, Jani & Kertész, János & Kaski, Kimmo, 2005. "Sandpiles on Watts–Strogatz type small-worlds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 535-547.
    5. Ouyang, Bo & Teng, Zhaosheng & Tang, Qiu, 2016. "Dynamics in local influence cascading models," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 182-186.
    6. 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.
    7. Linqing Liu & Weiran Wang & Xiaofei Yan & Mengyun Shen & Haizhi Chen, 2023. "The cascade influence of grain trade shocks on countries in the context of the Russia-Ukraine conflict," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-28, December.
    8. Chen, Zhichao & Zheng, Changjiang & Tao, Tongtong & Wang, Yanyan, 2024. "Reliability analysis of urban road traffic network under targeted attack strategies considering traffic congestion diffusion," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    9. Hou, Rui & Yang, Jianmei & Yao, Canzhong & McKelvey, Bill, 2015. "How does competition structure affect industry merger waves? A network analysis perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 140-156.
    10. Zhou, Jian & Coit, David W. & Felder, Frank A. & Tsianikas, Stamatis, 2023. "Combined optimization of system reliability improvement and resilience with mixed cascading failures in dependent network systems," Reliability Engineering and System Safety, Elsevier, vol. 237(C).

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