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A model for cascading failures in scale-free networks with a breakdown probability

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  • Wang, Jian-Wei
  • Rong, Li-Li

Abstract

Considering that not all overload nodes will be removed from networks due to some effective measures to protect them, we propose a new cascading model with a breakdown probability. Adopting the initial load of a node j to be Lj=[kj(∑m∈Γjkm)]α with kj and Γj being the degree of the node j and the set of its neighboring nodes, respectively, where α is a tunable parameter, we investigate the relationship between some parameters and universal robustness characteristics against cascading failures on scale-free networks. According to a new measure originated from a phase transition from the normal state to collapse, the numerical simulations show that Barabási–Albert (BA) networks reach the strongest robustness level against cascading failures when the tunable parameter α=0.5, while not relating to the breakdown probability. We furthermore explore the effect of the average degree 〈k〉 for network robustness, thus obtaining a positive correlation between 〈k〉 and network robustness. We then analyze the effect of the breakdown probability on the network robustness and confirm by theoretical predictions this universal robustness characteristic observed in simulations. Our work may have practical implications for controlling various cascading-failure-induced disasters in the real world.

Suggested Citation

  • Wang, Jian-Wei & Rong, Li-Li, 2009. "A model for cascading failures in scale-free networks with a breakdown probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1289-1298.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:7:p:1289-1298
    DOI: 10.1016/j.physa.2008.12.067
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    Citations

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    Cited by:

    1. Jin, Ziyang & Duan, Dongli & Wang, Ning, 2022. "Cascading failure of complex networks based on load redistribution and epidemic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    2. Yang, Guizhen & Qi, Xiaogang & Liu, Lifang, 2020. "Research on network robustness based on different deliberate attack methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Wang, Yingcong & Xiao, Renbin, 2016. "An ant colony based resilience approach to cascading failures in cluster supply network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 150-166.
    4. Kizhakkedath, A. & Tai, K., 2021. "Vulnerability analysis of critical infrastructure network," International Journal of Critical Infrastructure Protection, Elsevier, vol. 35(C).
    5. Ren, Hai-Peng & Song, Jihong & Yang, Rong & Baptista, Murilo S. & Grebogi, Celso, 2016. "Cascade failure analysis of power grid using new load distribution law and node removal rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 239-251.
    6. Zhu, Qian & Zhu, Zhiliang & Wang, Yifan & Yu, Hai, 2016. "Fuzzy-information-based robustness of interconnected networks against attacks and failures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 194-203.
    7. Zhou, Lin & Qi, Xiaogang & Liu, Lifang, 2023. "Robustness of networks with dependency groups considering fluctuating loads and recovery behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    8. Zhang, Wenping & Xia, Yongxiang & Ouyang, Bo & Jiang, Lurong, 2015. "Effect of network size on robustness of interconnected networks under targeted attack," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 80-88.
    9. Peng, Xingzhao & Yao, Hong & Du, Jun & Wang, Zhe & Ding, Chao, 2015. "Invulnerability of scale-free network against critical node failures based on a renewed cascading failure model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 69-77.
    10. Wang, Jianwei & Li, Yun & Zheng, Qiaofang, 2015. "Cascading load model in interdependent networks with coupled strength," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 242-253.
    11. Qi, Xiaogang & Yang, Guizhen & Liu, Lifang, 2020. "Robustness analysis of the networks in cascading failures with controllable parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    12. Tianhua Li & Yanchao Du & Yongbo Yuan, 2019. "Use of Variable Fuzzy Clustering to Quantify the Vulnerability of a Power Grid to Earthquake Damage," Sustainability, MDPI, vol. 11(20), pages 1-17, October.
    13. Hao, Yucheng & Jia, Limin & Wang, Yanhui, 2020. "Robustness of weighted networks with the harmonic closeness against cascading failures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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