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分析了快递超网络和电子元件超网络的相继故障扩散方式, 结合超图理论提出了2-section 图分析法和线图分析法, 并仿真分析了无标度超网络耦合映像格子的相继故障进程. 结果表明: 无标度超网络对外部攻击表现出了既鲁棒又脆弱的特性. 针对相继故障的不同扩散方式, 无标度超网络的相继故障行为表现出不同的特点. 超网络的相继故障行为和超网络的超度以及超边度分布有密切的联系, 也和超网络中超边的个数有关. 通过和同规模的Barabasi-Albert (BA)无标度网络对比, 在同一种攻击方式下同规模的无标度超网络都比BA 无标度网络表现出了更强的鲁棒性. 另外, 基于超边扩散的相继故障进程比基于节点扩散的相继故障进程更加缓慢.In this paper, we analyze the diffusion patterns of cascading failure, which happen in the express hypernetwork and electronic hypernetwork respectively. The cascading failure of the express hypernetwork is diffused by the node, and the cascading failure of the electronic hypernetwork is diffused by the hyper-edge. According to hyper-graph theory, we propose two methods to characterize these cascading failures, which are 2-section graph analytical method and line-graph analytical method. We analyze the characteristics of the cascading failures based on node by using the 2-section graph analytical method and based on hyper-edge by using line-graph analytical method, respectively. We construct a k uniform scale-free hypernetwork and analyze the cascading failure process of this hypernetwork based on the couple map lattice according to our methods. The simulation results show that the scale-free hypernetworks are both robust and vulnerable for attack. It is found that the cascading failure based on the node of k uniform scale-free hypernetwork is associated with the hyper-degree distribution of nodes, and the scale-free hypernetwork is robust for random attack and vulnerable for deliberate attack. The more nodes a hyper-edge has, the better robustness the hypernetwork has.The cascading failure based on the hyper-edge is different from the cascading failure based on the node. The cascading failure based on the hyper-edge is associated with the hyper-edge degree distribution. The hyper-edge degree distribution of the scale-free hypernetwork is not entirely the power-low distribution. When the cascading failure is diffused by the hyper-edge, the hypernetwork is vulnerable for random attack and robustness for deliberate attack if there are 3 or 5 nodes in a hyper-edge. Moreover, the hypernetwork becomes robust for the random attack if there are 7 nodes in a hyper-edge. Furthermore, the k uniform scale-free hypernetwork is more robust than the same size Barabasi-Albert scale-free network for the same attack. The cascading failure process based on the hyper-edge is slower than based on the node. We find that the edge number is another influential factor of robustness. The network is more robust if it has more edges for fixed node number. The line-graph has more edges than the 2-section graph in the same size scale-free hypernetwork, so the cascading failure of node is slower than that of hyper-edge.
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Keywords:
- hypergraph /
- scale-free hypernetwork /
- cascading failure /
- couple map lattice
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[1] Wang J J, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[2] Zhang Z K, Liu C 2010 J. Stat. Mech. -Theory E 2010 10005
[3] Krawiecki A 2013 Acta Phys. Polon. A 123
[4] Gmez-Gardees J, Reinares I, Arenas A, Flora L M 2012 Sci. Reports 2 620
[5] Hu F, Zhao H X, Ma X J 2013 Sci. Sin.: Phys. Mech. Astron. 43 16 (in Chinese) [胡枫, 赵海兴, 马秀娟 2013 中国科学: 物理学 力学 天文学 43 16]
[6] Hu F, Zhao H X, He J B, Li F X, Li S L, Zhang Z K 2013 Acta Phys. Sin. 62 198901 (in Chinese) [胡枫, 赵海兴, 何佳培, 李发旭, 李淑玲, 张子柯 2013 62 198901]
[7] Yang G Y, Liu J G 2014 Chin. Phys. B 23 018901
[8] Liu J G, Yang G Y, Hu Z L 2014 PLoS One 9 e89746
[9] Pei W D, Xia W, Wang Q L, et al. 2010 J. Univ. Sci. Technol. China 40 1186 (in Chinese) [裴伟东, 夏玮, 王全来 等 2010 中国科学技术大学学报 40 1186]
[10] Sorrentino F 2012 New J. Phys. 14 033035
[11] Wu Z Y, Duan J Q, Fu X C 2014 Appl. Math. Model 38 2961
[12] Krawiecki A 2014 Chaos, Soliton. Fract. 65 44
[13] Gmez S, Daz-Guilera A, Gmez-Gardees J, Prez-Vicente C J, Moreno Y, Arenas A 2013 Phys. Rev. Lett. 110 028701
[14] Wang J P, G Q, Yang G Y, Liu J G 2015 Physica A 428 250
[15] Yang G Y, Hu Z L, Liu J G 2015 Physica A 419 429
[16] Sol-Ribalta A, Domenico de M, Gmez S, Arenas A 2013 arXiv preprint arXiv:1506.07165 [physics.soc-ph]
[17] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[18] Dong G G, Gao J X, Du R J, Tian L X, Stanley H E, Havlin S 2013 Phys. Rev. E 87 052804
[19] Dong G G, Tian L X, Zhou D, Du R J, Xiao J, Stanley H E 2013 Euro. Lett. 102 68004
[20] Dong G G, Tian L X, Du R J, Stanley H E 2014 Physica A 394 370
[21] Segovia-Juarez J L, Colombano S, Kirschner D 2007 Biosystems 87 117
[22] Akram M, Dudek W A 2013 Inform. Sci. 218 182
[23] Rangasamy P, Akram M, Thilagavathi S 2013 Inform. Process. Lett. 113 599
[24] Segovia-Juarez J L, Colombano S 2003 BioSystems 68 187
[25] Berge C, Minieka E 1973 Graph and Hypergraph (North Holland: North-Holland Publishing Company Amsterdam) pp389-413
[26] Berge C, Sterboul F 1977 J. Comb. Theory B 22 97
[27] Estrada E, Rodrguez-Velzquez J A 2006 Physica A 364 581
[28] Volpentesta, A P 2008 Eur. J. Oper. Res. 188 390
[29] Pretolani D 2013 Eur. J. Oper. Res. 230 226
[30] Ghosal G, Zlatić V, Caldarelli G, Newman M E J 2009 Phys. Rev. E 79 066118
[31] Zlatić V, Ghoshal G, Caldarelli G 2009 Phys. Rev. E 80 036118
[32] Neubauer N, Obermayer K 2009 HT 09 Torino, Italy, June 29-July 1, 2009
[33] Bretto A 2013 Hypergraph Theory: An Introduction (New York: Springer Science Business Media)
[34] Peng X Z, Yao H, Du J, Wang Z, Ding C 2015 Acta Phys. Sin. 64 048901 (in Chinese) [彭兴钊, 姚宏, 杜军, 王哲, 丁超 2015 64 048901]
[35] Chen S M, L H, Xu Q G, Xu Y F, Lai Q 2015 Acta Phys. Sin. 64 048902 (in Chinese) [陈世明, 吕辉, 徐青刚, 许云飞, 赖强 2015 64 048902]
[36] Ding L, Zhang S Y 2012 Comput. Sci. 39 8 (in Chinese) [丁琳, 张嗣瀛 2012 计算机科学 39 8]
[37] Kanoko K 1992 Couple Map Lattice (Singapore: World Scientific)
[38] Wang X F, Xu J 2004 Phys. Rev. E 70 056113
[39] Xu J, Wang X F 2005 Physica A 349 685
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