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相依网络的相依模式(耦合模式)是影响其鲁棒性的重要因素之一. 本文针对具有无标度特性的两个子网络提出一种全局同质化相依网络耦合模式. 该模式以子网络的总度分布均匀化为原则建立相依网络的相依边, 一方面压缩度分布宽度, 提高其对随机失效的抗毁性, 另一方面避开对度大节点(关键节点)的相依, 提高其对蓄意攻击的抗毁性. 论文将其与常见的节点一对一的同配、异配及随机相依模式以及一对多随机相依模式作了对比分析, 仿真研究其在随机失效和蓄意攻击下的鲁棒性能. 研究结果表明, 本文所提全局同质化相依网络耦合模式能大大提高无标度子网络所构成的相依网络抗级联失效能力. 本文研究成果能够为相依网络的安全设计等提供指导意义.Many infrastructure networks interact with and depend on each other to provide proper functionality. The interdependence between networks has catastrophic effects on their robustness. Events taking place in one system can propagate to any other coupled system. Recently, great efforts have been dedicated to the research on how the coupled pattern between two networks affects the robustness of interdependent networks. However, how to dynamically construct the links between two interdependent networks to obtain stronger robustness is rarely studied. To fill this gap, a global homogenizing coupled pattern between two scale-free networks is proposed in this paper. Making the final degrees of nodes distributed evenly is the principle for building the dependency links, which has the following two merits. First, the system robustness against random failure is enhanced by compressing the broadness of degree distribution. Second, the system invulnerability against targeted attack is improved by avoiding dependence on high-degree nodes. In order to better investigate its efficiency on improving the robustness of coupled networks against cascading failures, we adopt other four kinds of coupled patterns to make a comparative analysis, i.e., the assortative link (AL), the disassortative link (DL), the random link (RL) and global random link (GRL). We construct the BA-BA interdependent networks with the above 5 coupled patterns respectively. After applying targeted attacks and random failures to the networks, we use the ratio of giant component size after cascades to initial network size to measure the robustness of the coupled networks. It is numerically found that the interdependent network based on global homogenizing coupled pattern shows the strongest robustness under targeted attacks or random failures. The global homogenizing coupled pattern is more efficient to avoid the cascading propagation under targeted attack than random failure. Finally, the reasonable explanations for simulation results is given by a simply graph. This work is very helpful for designing the interdependent networks against cascading failures.
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Keywords:
- coupled pattern /
- interdependent network /
- robustness /
- cascading failure
[1] Wang W X, Lai Y C, Dieter A 2011 Chaos 21 033112
[2] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
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[8] Nie T Y, Guo Z, Zhao K, Lu Z M 2015 Physica A 424 248
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[10] Moreira A A, Andrade Jr J S, Herrmann H J, Indekeu J O 2009 Phys. Rev. Lett. 102 018701
[11] Wang J W, Rong L L 2009 Safety Sci. 47 1332
[12] Rosato V, Issacharoff L, Tiriticco F, Meloni S, DePorcellinis S, Setola R 2008 Int. J. Crit. Infrastruct. 4 63
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[14] Vespignani A 2010 Nature 464 984
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[16] Buldyrev S V, Shere N W, Cwilich G A 2011 Phys. Rev. E 83 016112
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[18] Zhou D, Stanley H E, D'Agostino G, Scala A 2012 Phys. Rev. E 86 066103
[19] Wang J W, Chen J, Qian J F 2014 Physica A 393 535
[20] Cheng Z S, Cao J D 2015 Physica A 430 193
[21] 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 物理学报 63 028902]
[22] Wang J W, Yun L, Qiao F Z 2015 Physica A 430 242
[23] Chen Z, Du W B, Cao X B, Zhou X L 2015 Chaos, Solitons Fractals 80 7
[24] Shao J, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 036116
[25] 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 物理学报 64 048902]
[26] Wang J W, Jiang C, Qian J F 2013 Int. J. Mod. Phys. C 24 1350076
[27] Wang J W 2013 Physica A 392 2257
[28] Cao X B, Hong C, Du W B, Zhang J 2013 Chaos, Solitons Fractals 57 35
[29] Huang W, Chow TWS 2010 Chaos 20 033123
[30] Motter A E 2004 Phys. Rev. Lett. 93 098701
[31] Barabsi A L, Albert R 1999 Science 286 509
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[1] Wang W X, Lai Y C, Dieter A 2011 Chaos 21 033112
[2] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
[3] Mirzasoleiman B, Babaei M, Jalili M, Safari M 2011 Phys. Rev. E 84 046114
[4] Schfer M, Scholz J, Greiner M 2006 Phys. Rev. Lett. 96 108701
[5] Wang J W 2012 Nonlinear Dyn. 70 1959
[6] Yang R, Wang W X, Lai Y C, Chen G R 2009 Phys. Rev. E 79 026112
[7] Buzna L, Peters K, Ammoser H, Khnert C, Helbing D 2007 Phys. Rev. E 75 056107
[8] Nie T Y, Guo Z, Zhao K, Lu Z M 2015 Physica A 424 248
[9] Zhao L, Park K, Lai Y C, Ye N 2005 Phys. Rev. E 72 025104
[10] Moreira A A, Andrade Jr J S, Herrmann H J, Indekeu J O 2009 Phys. Rev. Lett. 102 018701
[11] Wang J W, Rong L L 2009 Safety Sci. 47 1332
[12] Rosato V, Issacharoff L, Tiriticco F, Meloni S, DePorcellinis S, Setola R 2008 Int. J. Crit. Infrastruct. 4 63
[13] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[14] Vespignani A 2010 Nature 464 984
[15] Wang J W, Rong L L 2009 Acta Phys. Sin. 58 3714 (in Chinese) [王建伟, 荣莉莉 2009 物理学报 58 3714]
[16] Buldyrev S V, Shere N W, Cwilich G A 2011 Phys. Rev. E 83 016112
[17] Parshani R, Rozenblat C, Ietri D, Ducruet C, Havlin S 2010 Europhys. Lett. 92 68002
[18] Zhou D, Stanley H E, D'Agostino G, Scala A 2012 Phys. Rev. E 86 066103
[19] Wang J W, Chen J, Qian J F 2014 Physica A 393 535
[20] Cheng Z S, Cao J D 2015 Physica A 430 193
[21] 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 物理学报 63 028902]
[22] Wang J W, Yun L, Qiao F Z 2015 Physica A 430 242
[23] Chen Z, Du W B, Cao X B, Zhou X L 2015 Chaos, Solitons Fractals 80 7
[24] Shao J, Buldyrev S V, Havlin S, Stanley H E 2011 Phys. Rev. E 83 036116
[25] 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 物理学报 64 048902]
[26] Wang J W, Jiang C, Qian J F 2013 Int. J. Mod. Phys. C 24 1350076
[27] Wang J W 2013 Physica A 392 2257
[28] Cao X B, Hong C, Du W B, Zhang J 2013 Chaos, Solitons Fractals 57 35
[29] Huang W, Chow TWS 2010 Chaos 20 033123
[30] Motter A E 2004 Phys. Rev. Lett. 93 098701
[31] Barabsi A L, Albert R 1999 Science 286 509
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