相互作用网络的攻击模型与渗流研究
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摘要
针对相互作用网络的蓄意攻击问题,本文提出了一种一般性的蓄意攻击模型,将该模型应用于2个完全随机耦合的ER网络与SF网络,并对渗流现象进行数值模拟与理论分析.本文主要结论为:相互作用网络较为脆弱,但对度大的和具有度大依赖顶点的顶点进行保护可以有效地提高整个相互作用网络的鲁棒性.具体表现为:1在耦合ER网络中,降低对度大顶点的攻击概率,对网络的破坏程度会降低,但攻击概率降低到一定程度后不再起作用;2在耦合SF网络中,发现需要同时保护2个网络的度大顶点,才能提高整个网络的鲁棒性;3对上面2种网络,即使同时保护2个网络的度大顶点,整个网络依然存在级联失效风险;4对混合ER-SF网络,需要同时保护2个网络的度大顶点,但保护ER网络的度大顶点更为有效.本文提出的蓄意攻击模型更符合实际相互作用网络的受攻击情况,对评估和研究相互作用网络具有重要的指导意义;同时,本文的研究结果在耦合网络的构建和维护等方面有着潜在的应用前景.
To study the targeted-attack problem in independent networks,we propose a general targetedattack model.Based on the oretical analysis and numerical simulations for two completely and randomly coupled ER networks in an investigation reported herein,we found that the independent networks were quite vulnerable,but their robustness could be improved by protecting the nodes with high degrees,or with high-degree independent nodes.Specifically,the results were:1 In the coupled ER networks,decreasing the attacking probability of high degree nodes would reduce the damage to the networks,yet no effect was observed when the attacking probability declined to a certain value.2 For the coupled SF networks,the robustness of the independent networks could be improved only by protecting the nodes with high degree simultaneously in the two networks.3 The above methods could not completely resolve the failure cascading,indicating the vulnerability of the independent networks.4 For the coupled ER-SF networks,the high-degree nodes of both networks should be simultaneously protected,though the low attacking probability of the nodes in ER networks was more efficient to improve the robustness.The targetedattack model described in this paper is more close to real attacking situations,thus can provide a valuable guide for the study of the robustness of actual independent networks.Moreover,the results are expected to be helpful for the construction and maintenance of independent networks.
To study the targeted-attack problem in independent networks,we propose a general targetedattack model.Based on the oretical analysis and numerical simulations for two completely and randomly coupled ER networks in an investigation reported herein,we found that the independent networks were quite vulnerable,but their robustness could be improved by protecting the nodes with high degrees,or with high-degree independent nodes.Specifically,the results were:1 In the coupled ER networks,decreasing the attacking probability of high degree nodes would reduce the damage to the networks,yet no effect was observed when the attacking probability declined to a certain value.2 For the coupled SF networks,the robustness of the independent networks could be improved only by protecting the nodes with high degree simultaneously in the two networks.3 The above methods could not completely resolve the failure cascading,indicating the vulnerability of the independent networks.4 For the coupled ER-SF networks,the high-degree nodes of both networks should be simultaneously protected,though the low attacking probability of the nodes in ER networks was more efficient to improve the robustness.The targetedattack model described in this paper is more close to real attacking situations,thus can provide a valuable guide for the study of the robustness of actual independent networks.Moreover,the results are expected to be helpful for the construction and maintenance of independent networks.
引文
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[14]SHAO J,BULDYREV S V,BRAUNSTEIN L A,et al.Structure of Shells in Complex Networks[J].Phys Rev E Stat Nonlin Soft Matter Phys,2009,80(3Pt 2):036105.
[2]LAPRIE J C,KANOUN K,KAA∧NICHE M.Modelling Interdependencies Between the Electricity and Information Infrastructures[J].Lecture Notes in Computer Science,2007(4680):54-67.
[3]PANZIERI S,SETOLA R.Failures Propagation in Critical Interdependent Infrastructures[J].International Journal of Modelling,Identification and Control,2008,3(1):69.
[4]BULDYREV S V,PARSHANI R,PAUL G,et al.Catastrophic Cascade of Failures in Interdependent Networks[J].Nature,2010,464(7291):1025-1028.
[5]PARSHANI R,BULDYREV S V,HAVLIN S.Interdependent Networks:Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition[J].Phys Rev Lett,2010,105(4):048701.
[6]HUANG X,GAO J,BULDYREV S V,et al.Robustness of Interdependent Networks Under Targeted Attack[J].Phys Rev E Stat Nonlin Soft Matter Phys,2011,83(6Pt 2):065101.
[7]DONG G,GAO J,TIAN L,et al.Percolation of Partially Interdependent Networks Under Targeted Attack[J].Phys Rev E Stat Nonlin Soft Matter Phys,2012,85(1Pt 2):016112.
[8]DONG G,GAO J,DU R,et al.Robustness of Network of Networks Under Targeted Attack[J].Phys Rev E Stat Nonlin Soft Matter Phys,2013,87(5):052804.
[9]GAO J,BULDYREV SV,HAVLIN S,et al.Robustness of a Network of Networks[J].Phys Rev Lett,2011,107(19):195701.
[10]GALLOS L K,COHEN R,ARGYRAKIS P,et al.Stability and Topology of Scale-Free Networks Under Attack and Defense Strategies[J].Phys Rev Lett,2005,94(18):188701.
[11]杨程成,杨春.相互作用网络耦合关系对其鲁棒性的影响[J].西南大学学报(自然科学版),2015,37(9):145-149.
[12]NEWMAN M E.Spread of Epidemic Disease on Networks[J].Phys Rev E Stat Nonlin Soft Matter Phys,2002,66(1Pt2):016128.
[13]SHAO J,BULDYREV S V,HAVLIN S,et al.Cascade of Failures in Coupled Network Systems with Multiple SupportDependence Relations[J].Phys Rev E Stat Nonlin Soft Matter Phys,2011,83(3Pt 2):036116.
[14]SHAO J,BULDYREV S V,BRAUNSTEIN L A,et al.Structure of Shells in Complex Networks[J].Phys Rev E Stat Nonlin Soft Matter Phys,2009,80(3Pt 2):036105.