复杂网络中带有应急恢复机理的级联动力学分析

李钊; 郭燕慧; 徐国爱; 胡正名

doi:10.7498/aps.63.158901

摘要

提出带有应急恢复机理的网络级联故障模型，研究模型在最近邻耦合网络，Erdos-Renyi随机网络，Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为. 给出了应急恢复机理和网络效率的定义，并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响. 结果表明，模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度，并且提高了网络的恢复能力. 而且网络中节点负载容量越大，网络效率降低速度和节点故障率的增长速度越慢. 同时，随着节点过载故障概率的减小，网络效率的降低速度和节点故障率的增长速度也逐渐减缓. 此外，对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析，结果发现网络拓扑节点度分布的异质化程度的增大，提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度. 以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为，为实际网络中级联故障现象的控制和防范提供了参考.

关键词:

Abstract

A model of cascading failures in complex networks with an emergency recovery mechanism is proposed in this paper, and the cascading dynamics is investigated by running the proposed model on nearest-neighbor coupled network, Erdos-Renyi random graph network, Watts-Strogatz small-world network and Barabasi-Albert scale-free network respectively. New concepts in emergency recovery mechanism and the efficiency of networks are defined. And the effects of the parameters on the network efficiency and failure rate are investigated. Results demonstrate that the increase of the emergency recovery probability would reduce the network efficiency decreasing speed and the failure rate growing speed, and also improve the resilience of the network. And the greater the load capacity of the nodes in the network, the slower the speeds of network efficiency reducing and failure rate growing. Meanwhile, with the decrease of the overload node failure probability, the reducing speed of network efficiency and the growing speed of failure rate would reduce gradually. Furthermore, the changes of the network efficiency and failure rate during the process of cascading failures in different network topologies are analyzed. It is found that the rise of the heterogeneity of degree distribution increases the reducing speed of network efficiency and the growing speed of failure rate. All these results can help analyze the cascading dynamics in complex networks with an emergency recovery mechanism, and may provide a guidance for the controling of cascading failures and protecting against them in real-life complex networks.

Keywords:

作者及机构信息

1.
北京邮电大学信息安全中心; 北京邮电大学灾备技术国家工程实验室, 北京 100876

基金项目: 国家自然科学基金（批准号：60970135，61170282）、高等学校博士学科点专项科研基金（批准号：20120005110017）、国家教育部优秀青年教师基金（批准号：2013RC0312）和国家科技支撑计划（批准号：2012BAH06B02）资助的课题.

Authors and contacts

1.
Information Security Center, Beijing University of Posts and Telecommunications; National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 60970135, 61170282), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120005110017), the Science Foundation for the Excellent Youth Scholars of Ministry of Education of China (Grant No. 2013RC0312), and the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2012BAH06B02).

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施引文献

[1]	Wang J W, Rong L L 2009 Physica A 388 1289
[2]
[3]	Heide D, Schafer M, Greiner M 2008 Phys. Rev. E 77 056103
[4]
[5]	Bao Z J, Gao Y J, Ding L J, Wang G Z, Han Z X 2008 Physica A 387 5922
[6]
[7]
[8]	Simonsen I, Buzna L, Peters K, Bornholdt S, Helbing D 2008 Phys. Rev. Lett. 100 218701
[9]	Li P, Wang B H, Sun H, Gao P, Zhou T 2008 Eur. Phys. J. B 62 1
[10]
[11]	Bao Z J, Cao Y J, Ding L J, Han Z X, Wang G Z 2008 Phys. Lett. A 372 5778
[12]
[13]	Wang X F, Xu J 2004 Phys. Rev. E 70 056113
[14]
[15]	Kinney R, Crucitti P, Albert R, Latora V 2005 Eur. Phys. J. B 46 101
[16]
[17]
[18]	Crucitti P, Latora V, Marchiori M 2004 Phys. Rev. E 69 045104
[19]
[20]	Zhao L, Park K, Lai Y C 2004 Phys. Rev. E 70 035101
[21]	Goh K I, Kahng B, Kim D 2002 Phys. Rev. Lett. 88 108701
[22]
[23]
[24]	Zhao L, Park K, Lai Y C, Ye N 2005 Phys. Rev. E 72 025104
[25]
[26]	Wu J J, Gao Z Y, Sun H J 2007 Physica A 378 505
[27]
[28]	Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[29]	Goh K I, Lee D S, Kahng B, Kim D 2003 Phys. Rev. Lett. 91 148701
[30]
[31]	Moreno Y, Gomez J B, Pacheco A F 2002 Europhys. Lett. 58 630
[32]
[33]	Wang W X, Chen G R 2008 Phys. Rev. E 77 026101
[34]
[35]	Motter A E 2004 Phys. Rev. Lett. 93 098701
[36]
[37]	Zhao H, Gao Z Y 2007 Eur. Phys. J. B 57 95
[38]
[39]	Sun H J, Zhao H, Wu J J 2008 Physica A 387 6431
[40]
[41]	Ash A, Newth D 2007 Physica A 380 673
[42]
[43]
[44]	Wang J W, Rong L L 2009 Physica A 388 1731
[45]	Latora V, Marchiori M 2001 Phys. Rev. Lett. 87 198701
[46]
[47]
[48]	Li Y, Lv L, Luan L 2009 Acta Phys. Sin. 58 4463 (in Chinese) [李岩, 吕翎, 栾玲 2009 58 4463]
[49]	Xu Q X, Xu X J 2009 Chin. Phys. B 18 933
[50]
[51]
[52]	Li T, Pei W J, Wang S P 2009 Acta Phys. Sin. 58 5903 (in Chinese) [李涛, 裴文江, 王少平 2009 58 5903]
[53]
[54]	Chen H L, Liu Z X, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 6068 (in Chinese) [陈华良, 刘忠信, 陈增强, 袁著祉 2009 58 6068]
[55]	Tian L, Di Z R, Yao H 2011 Acta Phys. Sin. 60 028901 (in Chinese) [田柳, 狄增如, 姚虹 2011 60 028901]
[56]
[57]	Wang J, Liu Y H, Zhu J Q, Jiao Y 2008 J Zhejiang Univ Sci A 9 101331
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[59]	Barabsi A L, Bonabeau E 2003 Scientific American 5 50
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[61]	Newman M E J 2003 SIAM Review 45 167
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[69]	Li Z, Xu G A, Ban X F, Zhang Y, Hu Z M 2013 Acta Phys. Sin. 62 200203 (in Chinese) [李钊, 徐国爱, 班晓芳, 张毅, 胡正名 2013 62 200203]
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