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利用典型的Barabási-Albert无标度网络构建了基于度的正/负相关相依网络模型, 该模型考虑子网络间的相依方式及相依程度, 主要定义了两个参数F和K, F表示相依节点比例, K表示相依冗余度. 在随机攻击及基于度的蓄意攻击模式下, 针对网络的级联失效问题, 研究了不同的F值和K值对该相依网络模型鲁棒性的影响, 与随机相依网络模型进行了对比研究. 仿真结果表明:无论是随机相依或是基于度的正/负相关相依网络, 其鲁棒性都是随着F的增大而减弱, 随着K的增大而增强; 在随机攻击下, 全相依模式(F=1)时, 基于度正相关相依网络模型鲁棒性最优, 部分相依模式 (F =0.2, 0.5, 0.8)时, 基于度的负相关相依网络模型则表现出更好的鲁棒性. 而在基于度的蓄意攻击下, 无论F为何值, 基于度的正相关相依网络模型表现出弱鲁棒性.The model of interdependent network based on positive/negative correlation of the degree is constructed by the typical Barabási-Albert network in this paper. Dependency modality and dependency degree are considered in the model. Two parameters F and K are defined, which represent the proportion of dependency node and the redundancy of dependency, respectively. We study the influences of different values of F and K on the robustness of interdependent network in cascading failures under degree-based attacks and random attacks and also compare the results with those from the random interdependent network model. The simulation results show that the robustness of both random independency and interdependent network based on positive/negative correlation of the degree decreases as F increases and increases as K increases; in the model of full interdependence (F = 1), the robustness of interdependent network based on positive correlation of the degree is optimal under random attacks; the interdependent network based on negative correlation of the degree shows stronger robustness in the model of partial interdependence (F= 0.2, 0.5, 0.8). While the interdependent network based on positive correlation of the degree shows poorer robustness with any value of F under degree-based attacks.
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Keywords:
- interdependent network /
- dependency degree /
- robustness /
- cascading failure
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[1] Hu Y, Ksherim B, Cohen R, Havlin S 2011 Phys. Rev. E 84 066116
[2] Morris R G, Barthelemy M 2012 Phys. Rev. Lett. 109 128703
[3] Buldyrev S V, Shere N W, Cwilich G A 2011 Phys. Rev. E 83 016112
[4] Albert R, Albert I, Nakarado G L 2004 Phys. Rev. E 69 025103
[5] Shen Y, Pei W J, Wang K, Wang S P 2009 Chin. Phys. B 18 3783
[6] Gong Z Q, Wang X J, Zhi R, Feng A X 2011 Chin. Phys. B 20 079201
[7] Cohen R, Erez K, Ben-Avraham D, Havlin S 2000 Phys. Rev. Lett. 85 4626
[8] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
[9] Cohen R, Erez K, Ben-Avraham D, Havlin S 2001 Phys. Rev. Lett. 86 3682
[10] Zhang Z Z, Xu W J, Zeng S Y, Lin J R 2014 Chin. Phys. B 23 088902
[11] Shi B Y, Liu J M 2012 IEEE Trans. Syst. Man Cy. B 42 1369
[12] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 61 170512]
[13] Xiao Y D, Lao S Y, Hou L L, Bai L 2013 Acta Phys. Sin. 62 180201 (in Chinese) [肖延东, 老松杨, 侯绿林, 白亮 2013 62 180201]
[14] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[15] Rinaldi S M, Peerenboom J P, Kelly T K 2001 IEEE Control Syst. 21 11
[16] Gao J, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. Lett. 107 195701
[17] Parshani R, Buldyrev S V, Havlin S 2010 Phys. Rev. Lett. 105 048701
[18] Shao J, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 036116
[19] Li W, Bashan A, Buldyrev S V, Stanley H E, Havlin S 2012 Phys. Rev. Lett. 108 228702
[20] Gao J X, Buldyrev S V, Stanly H E, Hanlin S 2012 Nat. Phys. 8 40
[21] Li G Y, Cheng B S, Zhang P, Li D Q 2013 J. Univ. Electron. Sci. Technol. China 42 23 (in Chinese) [李国颖, 成柏松, 张 鹏, 李大庆 2013 电子科技大学学报 42 23]
[22] Huang X Q, Gao J X, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 065101
[23] Zhou D, Agostino G D, Scala A, Stanley H E 2012 Phys. Rev. E 86 066103
[24] Donges J F, Schultz H C H, Marwan N, Zou Y, Kurths J 2011 Eur. Phys. J. B 84 635
[25] Shai S, Dobson S 2012 Phys. Rev. E 86 066120
[26] Chen S M, Zou X Q, L H, Xu Q G 2014 Acta Phys. Sin. 63 028902 (in Chinese) [陈世明, 邹小群, 吕辉, 徐青刚 2014 63 028902]
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