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为了深入研究复杂网络抵制连锁故障的全局鲁棒性，针对现实网络上的负载重分配规则常常是介于全局分配与最近邻分配、均匀分配与非均匀分配的特点，围绕负荷这一影响连锁故障发生和传播最重要的物理量以及节点崩溃后的动力学过程，提出了一种可调负载重分配范围与负载重分配异质性的复杂网络连锁故障模型，并分析了该模型在无标度网络上的连锁故障条件. 数值模拟获得了复杂网络抵制连锁故障的鲁棒性与模型中参数的关系. 此外，基于网络负载分配规则的分析以及理论解析的推导，验证了数值模拟结论，也证明在最近邻与全局分配两种规则下都存在负载分配均匀性参数等于初始负荷强度参数即β = τ 使得网络抵御连锁故障的能力最强.To better explore the robustness against cascading failures on complex networks, according to the redistribution rule of the real networks always lie between global preferential rule and local preferential rule or between even shared rule and extremely heterogeneous rule. A new cascading model is proposed based on a tunable load redistribution model. It can tune the load redistribution range and the redistribution heterogeneity of extra load respectively by a redistribution range coefficient and a redistribution heterogeneity coefficient. With this model, we further investigate cascading failures on scale-free networks in terms of numerical simulation and theoretical analysis respectively. Numerical simulation and analytic results show that the model can achieve better robustness against cascading failure than the previous model by adjusting the redistribution range and heterogeneity.
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Keywords:
- complex network /
- cascading failure /
- load redistribution /
- robustness
[1] 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]
[2] Xia Y X, Fan J, Hill D 2010 Phys. A 389 1281
[3] Sergey V B, Roni P, Gerald P, Eugene Stanley H, Shlomo H 2010 Nature 464 08932
[4] Wang J W 2012 Phys. A 391 4004
[5] Wang J W 2012 Complexity 17 17
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[8] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[9] Wu Z H, Fang H J 2008 Chin. Phys. Lett. 25 3822
[10] Zheng J F, Gao Z Y, Fu B B, Li F 2009 Chin. Phys. B 18 4754
[11] Hu K, Hu T, Tang Y 2010 Chin. Phys. B 19 080206
[12] Wang B, Kim B J 2007 Euro. Phys. Lett 78 48001
[13] Li P, Wang B H, Sun H 2008 Euro. Phys. J. B 62
[14] Dobson I, Carreras B A, Lynch V E 2007 Chaos 2 026103
[15] Kim D H, Kim B J, Jeong H 2005 Phys. Rev. Lett. 94 025501
[16] Jorg L, Jakob B 2010 Phys. Rev. E 81 031129
[17] Wang W X, Chen G R 2008 Phys. Rev. E 77 026101
[18] Wu Z X, G. Peng, Wang W X, Chan S, Wong E E M 2008 J. Stat. Mech. P 05013
[19] Wang J W, Rong L L 2009 Acta Phys. Sin. 58 3714 (in Chinese) [王建伟, 荣莉莉 2009 58 3714]
[20] Wang J W, Rong L L 2009 Phys. A 388 1289
[21] Wang J W, Rong L L, Zhang L, Zhang Z Z 2008 Phys. A 387 6671
[22] Wang J W, Rong L L 2009 Safety Sci. 47 1332
[23] Wang J W, Rong L L 2011 Safety Sci. 49 807
[24] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
[25] Barabási A L, Albert R 1999 Science 286 509
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[1] 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]
[2] Xia Y X, Fan J, Hill D 2010 Phys. A 389 1281
[3] Sergey V B, Roni P, Gerald P, Eugene Stanley H, Shlomo H 2010 Nature 464 08932
[4] Wang J W 2012 Phys. A 391 4004
[5] Wang J W 2012 Complexity 17 17
[6] Crucitti P, Latora V, Marchiori M 2004 Phys. Rev. E 69 045104
[7] Motter A E 2004 Phys. Rev. Lett. 93 098701
[8] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[9] Wu Z H, Fang H J 2008 Chin. Phys. Lett. 25 3822
[10] Zheng J F, Gao Z Y, Fu B B, Li F 2009 Chin. Phys. B 18 4754
[11] Hu K, Hu T, Tang Y 2010 Chin. Phys. B 19 080206
[12] Wang B, Kim B J 2007 Euro. Phys. Lett 78 48001
[13] Li P, Wang B H, Sun H 2008 Euro. Phys. J. B 62
[14] Dobson I, Carreras B A, Lynch V E 2007 Chaos 2 026103
[15] Kim D H, Kim B J, Jeong H 2005 Phys. Rev. Lett. 94 025501
[16] Jorg L, Jakob B 2010 Phys. Rev. E 81 031129
[17] Wang W X, Chen G R 2008 Phys. Rev. E 77 026101
[18] Wu Z X, G. Peng, Wang W X, Chan S, Wong E E M 2008 J. Stat. Mech. P 05013
[19] Wang J W, Rong L L 2009 Acta Phys. Sin. 58 3714 (in Chinese) [王建伟, 荣莉莉 2009 58 3714]
[20] Wang J W, Rong L L 2009 Phys. A 388 1289
[21] Wang J W, Rong L L, Zhang L, Zhang Z Z 2008 Phys. A 387 6671
[22] Wang J W, Rong L L 2009 Safety Sci. 47 1332
[23] Wang J W, Rong L L 2011 Safety Sci. 49 807
[24] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
[25] Barabási A L, Albert R 1999 Science 286 509
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