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研究负荷作用下相依网络中的级联故障具有重要的现实意义, 可为提高相依网络的鲁棒性提供参考. 构建了双层相依网络级联故障模型, 主要研究了外部度和内部度对负荷贡献比、耦合因素、层内度-度相关性对相依网络级联故障的影响. 研究表明, 当外部度和内部度对负荷贡献比达到一定值时, 相依网络抵抗级联故障的鲁棒性最强. 而耦合因素的影响是多方面的, 为了达到较高鲁棒性, 建议采用异配耦合方式和尽可能大的平均外部度, 并尽量使外部度保持均匀分布. 另外, 与不考虑负荷作用时相反, 当表征层内度-度相关性的相关系数越大时, 其抵抗级联故障的能力越强.The study of load-induced cascading failures in interdependent networks is of great realistic significance, which can provide valuable reference for designing high robust interdependent network or improving their robustness. In this paper, we establish a cascading model for a double layer interdependent network, and study the effects of the contributions of inter-degree and intra-degree to the loads, the coupling, and the intra-node linking similarity on the cascading failure in the interdependent network. Our studies show that when the contributions of inter-degree and intra-degree to the loads attain some values, the interdependent network reaches the highest robustness against cascading failures. As a notable feature for the interdependent network that is different from an isolated network, the coupling must have a significant influence on cascading failure in the interdependent network. In order to reach higher robustness, we suggest that the disassortative coupling be used and the inter-degree be made as homogeneous as possible under condition that a larger average inter-degree is adopted. In addition, we find that it is contrary to the case of neglecting loads that when the Pearson correlation coefficient for measuring the intra-layer degree-degree relation is larger, the interdependent network is more robust against cascading failures.
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Keywords:
- interdependent networks /
- cascading failure /
- load-induced /
- robustness
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[1] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwanga D U 2006 Phys. Rep. 424 175
[2] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[3] Crucitti P, Latora V, Marchiori M 2004 Phys. Rev. E 69 045104(R)
[4] Wang J W, Rong L L 2009 Physica A 388 1289
[5] Wang J W, Rong L L 2009 Acta Phys. Sin. 58 3714 (in Chinese) [王建伟, 荣莉莉 2009 58 3714]
[6] Zhang J F, Yang L X, Gao Z Y 2010 Int. J. Mod. Phys. C 21 991
[7] Motter A E 2004 Phys. Rev. Lett. 93 098701
[8] Zhao L, Park K, Lai Y C 2004 Phys. Rev. E 70 035101(R)
[9] Wang J W, Rong L L, Zhang L, Zhang Z Z 2008 Physica A 387 6671
[10] Wei D Q, Luo X S, Zhang B 2012 Physica A 391 2771
[11] Ash J, Newth D 2007 Physica A 380 673
[12] Li P, Wang B H, Sun H, Gao P, Zhou T 2008 Eur. Phys. J. B 62 101
[13] Dou B L, Wang X G, Zhang S Y 2010 Physica A 389 2310
[14] Hu K, Hu T, Tang Y 2010 Chin. Phys. B 19 080206
[15] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[16] Parshani R, Buldyrev S V, Havlin S 2010 Phys. Rev. Lett. 105 048701
[17] Shao J, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 036116
[18] Huang X Q, Gao J X, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 065101(R)
[19] Buldyrev S V, Shere N W, Cwilich G A 2011 Phys. Rev. E 83 016112
[20] Zhou D, Stanley H E, D'Agostino G, Scala A 2012 Phys. Rev. E 86 066103
[21] Gao J X, Buldyrev S V, Stanley H E, Havlin S 2012 Nat. Phys. 8 40
[22] Zhou D, Gao J X, Havlin S, Stanley H E 2013 Phys. Rev. E 87 052812
[23] Shao S, Huang X Q, Stanley H E, Havlin S 2014 Phys. Rev. E 89 032812
[24] Barabási A L, Albert R 1999 Science 286 509
[25] Zio E, Sansavini G 2011 IEEE. Trans. Reliab. 60 94
[26] Brummitt C D, D'Souza R M, Leicht E A 2012 PNAS 109 E680
[27] Qiu Y Z 2013 Physica A 392 1920
[28] Peng X Z, Yao H, Du J, Ding C, Zhang Z H 2014 Acta Phys. Sin. 63 078901 (in Chinese) [彭兴钊, 姚宏, 杜军, 丁超, 张志浩 2014 63 078901]
[29] Goh K I, Kahng B, Kim D 2001 Phys. Rev. Lett. 87 278701
[30] Barthélemy M 2004 Euro. Phys. J. B 38 163
[31] Tan F, Xia Y X, Zhang W P, Jin X Y 2013 Europhys. Lett. 102 28009
[32] Newman M E J 2010 Networks: an Introduction (New York: Oxford University Press)
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