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Liu and Barabasi applied the modern control theory to the network controllability of linear dynamical systems and proposed a method to calculate the minimal set of driver node which controls the states of all nodes in a linear time invariant complex network with any topology. The network controllability model solves the computable problems of the network controllability. Facing the problem of node overloaded failure in real networks, in the paper we investigate the model of network controllability based on node overloaded failure. Through the simulation of betweenness and Weibull failure model, the results demonstrate that the difficulty in maintaining the controllability of SF network is significantly greater than that of ER network. In the target failure mechanism, even if the failure signals input rarely to the networks, they can greatly increase the difficulty of network controllability. Besides, the node failure based high betweenness centrality is more efficient than failure based high degree on damaging network controllability, which indicates the nodes with high betweenness centrality play an important role in maintaining the network controllability. Furthermore, taking the reasonable measures for different load failure model can prevent the networks from inducing a step uncontrollable phenomenon.
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Keywords:
- network controllability /
- structure controllability /
- node failure
[1] Lombardi A, Hörnquist M 2007 Phys. Rev. E 75 056110
[2] Sorrentino F, Bernardo M, Garofalo F, Chen G R 2007 Phys. Rev. E 75 046103
[3] Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167
[4] Mller F J, Schuppert A 2011 Nature 478 E4
[5] Egerstedt M 2011 Nature 473 158
[6] Hou L L, Lao S Y, Liu G, Bai L 2012 Chin. Phys. Lett. 29 108901
[7] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[8] 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 物理学报 61 170512]
[9] Lin C T 1974 IEEE Trans. Automatic Control 19 201
[10] Bollobás B 1985 Random Graphs (London: Academic)
[11] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[12] Motter A E 2004 Phys. Rev. Lett. 93 098701
[13] Newman M E J 2001 Proc. Natl. Acad. Sci. 98 404
[14] Moreno Y, Gómez B J, Pacheco A F 2002 Europhys. Lett. 58 630
[15] Erdös P, Rényi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[16] Barabási A L, Albert R 1999 Science 286 509
[17] Pu C L, Pei W J, Andrew M 2012 Physica A 391 4420
[18] Freeman L C 1977 Sociometry 40 35
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[1] Lombardi A, Hörnquist M 2007 Phys. Rev. E 75 056110
[2] Sorrentino F, Bernardo M, Garofalo F, Chen G R 2007 Phys. Rev. E 75 046103
[3] Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167
[4] Mller F J, Schuppert A 2011 Nature 478 E4
[5] Egerstedt M 2011 Nature 473 158
[6] Hou L L, Lao S Y, Liu G, Bai L 2012 Chin. Phys. Lett. 29 108901
[7] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[8] 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 物理学报 61 170512]
[9] Lin C T 1974 IEEE Trans. Automatic Control 19 201
[10] Bollobás B 1985 Random Graphs (London: Academic)
[11] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[12] Motter A E 2004 Phys. Rev. Lett. 93 098701
[13] Newman M E J 2001 Proc. Natl. Acad. Sci. 98 404
[14] Moreno Y, Gómez B J, Pacheco A F 2002 Europhys. Lett. 58 630
[15] Erdös P, Rényi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[16] Barabási A L, Albert R 1999 Science 286 509
[17] Pu C L, Pei W J, Andrew M 2012 Physica A 391 4420
[18] Freeman L C 1977 Sociometry 40 35
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