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Attack robustness of cascading model with node weight

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Abstract

Considering the node weight and the effect of the neighboring nodes, we introduce a method to define the initial load of a node in a network and propose a cascading model. Our aim is to explore how to allocate the initial load and select some nodes to be protected so as to maximize the network robustness against cascading failures. According to the distribution of the node weight and the normalized effect of the neighboring nodes, we focus on investigating different roles of high-load and low-load nodes and the correlation between some parameters in our model and the strongest robust level of a network against cascading failures. We obtain by the numerical simulations the optimal values of the parameters in our model at which the network can reach the strongest robust level against cascading failures. In addition, we find that the effect of two attacks strongly depends on the parameters of the node weight and the normalized effect of the neighboring nodes, i.e., the network robustness of attacking the low-load nodes has a positive correlation with the parameter of the node weight, while has a negative correlation with the parameter of the normalized reaction of the neighboring nodes. While the result of attacking the high-load nodes is almost on the contrary. Finally, we verify the numerical results by the theoretical analysis.

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References

  1. Rosato, V., Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S., Setola, R.: Modelling interdependent infrastructures using interacting dynamical models. Int. J. Crit. Infrastruct. 4, 63C79 (2008)

    Article  Google Scholar 

  2. Albert, R., Albert, I., Nakarado, G.L.: Structural vulnerability of the North American power grid. Phys. Rev. E 69, 025103(R) (2004)

    Article  Google Scholar 

  3. Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the Internet. Phys. Rev. Lett. 87, 258701 (2001)

    Article  Google Scholar 

  4. Chang, L., Wu, Z.G.: Performance and reliability of electrical power grids under cascading failures. Int. J. Electr. Power 33(8), 1410–1419 (2011)

    Article  MathSciNet  Google Scholar 

  5. Wang, J.W., Rong, L.L.: Cascade-based attack vulnerability on the US power grid. Saf. Sci. 47(10), 1332–1336 (2009)

    Article  Google Scholar 

  6. Leonardo, D.-O., Srivishnu, M.V.: Cascading failures in complex infrastructure systems. Struct. Saf. 31, 157–167 (2009)

    Article  Google Scholar 

  7. Ricard, V.S., Martí, R.C., Bernat, C.M., Sergi, V.: Robustness of the European power grids under intentional attack. Phys. Rev. E 77, 026102 (2008)

    Google Scholar 

  8. Wang, J.W.: Robustness of complex networks with the local protection strategy against cascading failures. Saf. Sci. 53, 219–225 (2013)

    Article  Google Scholar 

  9. Goh, K.I., Hahng, B., Kim, D.: Fluctuation-driven dynamics of the Internet topology. Phys. Rev. Lett. 88(10), 108701 (2002)

    Article  Google Scholar 

  10. Zhang, G.D., Li, Z., Zhang, B., Halang, W.A.: Understanding the cascading failures in Indian power grids with complex networks theory. Phys. A 392, 3273–3280 (2013)

    Article  Google Scholar 

  11. Wang, W.X., Lai, Y.C., Dieter, A.: Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks. Chaos 21(3), 033112 (2011)

    Article  Google Scholar 

  12. Crucitti, P., Latora, V., Marchiori, M.: Model for cascading failures in complex networks. Phys. Rev. E 69, 045104 (2004)

    Article  Google Scholar 

  13. Mirzasoleiman, B., Babaei, M., Jalili, M., Safari, M.: Cascaded failures in weighted networks. Phys. Rev. E 84, 046114 (2011)

    Article  Google Scholar 

  14. Wang, J.W., Rong, L.L., Zhang, L., Zhang, Z.Z.: Attack vulnerability of scale-free networks due to cascading failures. Phys. A 387(26), 6671–6678 (2008)

    Article  Google Scholar 

  15. Vespignani, A.: The fragility of interdependency. Nature 464, 984–985 (2010)

    Article  Google Scholar 

  16. Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., Havlin, S.: Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010)

    Article  Google Scholar 

  17. Gao, J., Buldyrev, S.V., Stanley, H.E., Havlin, S.: Networks formed from interdependent networks. Nat. Phys. 8, 40–48 (2012)

    Article  Google Scholar 

  18. Gao, J., Buldyrev, S.V., Havlin, S., Stanley, H.E.: Robustness of a network of networks. Phys. Rev. Lett. 107(19), 195701 (2011)

    Article  Google Scholar 

  19. Brummitt, C.D., D’souza, R.M., Leicht, E.A.: Suppressing cascades of load in interdependent networks. Proc. Natl. Acad. Sci. USA 109(12), E680–E689 (2012)

    Article  Google Scholar 

  20. Shao, J., Buldyrev, S.V., Havlin, S., Stanley, H.E.: Cascade of failures in coupled network systems with multiple support-dependence relations. Phys. Rev. E 83(3), 036116 (2011)

    Article  MathSciNet  Google Scholar 

  21. Qiu, Y.Z.: Cascading dynamics with local weighted flow redistribution in interdependent networks. Eur. Phys. J. B 86, 329 (2013)

    Article  MathSciNet  Google Scholar 

  22. 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. Phys. Rev. Lett. 105(4), 048701 (2010)

    Article  Google Scholar 

  23. Huang, X.Q., Gao, J.X., Buldyrev, S.V., havlin, S., Stanley, H.E.: Robustness of interdependent networks under targeted attack. Phys. Rev. E 83(6), 065101(R) (2011)

    Article  Google Scholar 

  24. Schäfer, M., Scholz, J., Greiner, M.: Proactive Robustness Control of Heterogeneously Loaded Networks. Phys. Rev. Lett. 96(10), 108701 (2006)

    Article  Google Scholar 

  25. Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Phys. Rev. Lett. 100(21), 218701 (2008)

    Article  Google Scholar 

  26. Ash, A., Newth, D.: Optimizing complex networks for resilience against cascading failure. Phys. A 380, 673–683 (2007)

    Article  Google Scholar 

  27. Wang, B., Kim, B.J.: A high-robustness and low-cost model for cascading failures. Europhys. Lett. 78(4), 48001 (2007)

  28. Cao, X.B., Hong, C., Du, W.B., Zhang, J.: Improving the network robustness against cascading failures by adding links. Chaos Soliton Fract. 57, 35–40 (2013)

    Article  Google Scholar 

  29. Wang, J.W.: Mitigation of cascading failures on complex networks [J]. Nonlinear Dyn. 70(3), 1959–1967 (2012)

    Article  Google Scholar 

  30. Yang, R., Wang, W.X., Lai, Y.C., Chen, G.R.: Optimal weighting scheme for suppressing cascades and traffic congestion in complex networks. Phys. Rev. E 79(2), 026112 (2009)

    Article  Google Scholar 

  31. Pahwa, S., Youssef, M., Schumm, P., Scoglio, C., Schulz, N.: Optimal intentional islanding to enhance the robustness of power grid networks. Phys. A 392, 3741–3754 (2013)

    Article  MathSciNet  Google Scholar 

  32. Buzna, L., Peters, K., Ammoser, H., Kühnert, C., Helbing, D.: Efficient response to cascading disaster spreading. Phys. Rev. E 75(5), 056107 (2007)

    Article  Google Scholar 

  33. Wang, W.X., Chen, G.R.: Universal robustness characteristic of weighted networks against cascading failure. Phys. Rev. E 77, 026101 (2008)

    Article  Google Scholar 

  34. Wu, Z.X., Peng, G., Wang, W.X., Chan, S., Wong, E.E.M.: Cascading failure spreading on weighted heterogeneous networks. J. Stat. Mech. 2008, P05013 (2008)

    Google Scholar 

  35. Wang, S.L., Hong, L., Ouyang, M., Zhang, J.H., Chen, X.G.: Vulnerability analysis of interdependent infrastructure systems under edge attack strategies. Saf. Sci. 51, 328–337 (2013)

    Article  Google Scholar 

  36. Zhao, L., Park, K., Lai, Y.C.: Attack vulnerability of scale-free networks due to cascading breakdown. Phys. Rev. E 70(3), 035101(R) (2004)

    Article  Google Scholar 

  37. Zhao, L., Park, K., Lai, Y.C., Ye, N.: Tolerance of scale-free networks against attack-induced cascades. Phys. Rev. E 72(2), 025104 (2005)

    Article  Google Scholar 

  38. Moreira, A.A., Andrade Jr, J.S., Herrmann, H.J., Indekeu, J.O.: How to Make a Fragile Network Robust and Vice Versa. Phys. Rev. Lett. 102(1), 018701 (2009)

    Article  Google Scholar 

  39. Li, S.D., Li, L.X., Yang, Y.X., Luo, Q.: Revealing the process of edge-based-attack cascading failures. Nonlinear Dyn. 69, 837–845 (2012)

    Article  MathSciNet  Google Scholar 

  40. Wang, J.W., Rong, L.L.: Edge-based-attack induced cascading failures on scale-free networks. Phys. A 388(8), 1731–1737 (2009)

    Article  Google Scholar 

  41. Wang, J.W., Rong, L.L.: Robustness of the western United States power grid under edge attack strategies due to cascading failures. Saf. Sci. 49(6), 807–812 (2011)

    Article  MathSciNet  Google Scholar 

  42. Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant nos. 71101022 and 71102119, the Fundamental Research Funds for the Central Universities under Grant No. N110406003, and the Program for New Century Excellent Talents in University under Grant no. NCET-12-0100.

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Authors and Affiliations

  1. School of Business Administration, Northeastern University, Shenyang , 110819, People’s Republic of China

    Jianwei Wang, Chuan Zhang, Yi Huang & Chong Xin

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  1. Jianwei Wang
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  2. Chuan Zhang
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  3. Yi Huang
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  4. Chong Xin
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Correspondence to Jianwei Wang.

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Wang, J., Zhang, C., Huang, Y. et al. Attack robustness of cascading model with node weight. Nonlinear Dyn 78, 37–48 (2014). https://doi.org/10.1007/s11071-014-1420-3

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