Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:A3L-B

Session:

Number:166

On the Dynamics of Cascading Failures in Interdependent Networks

Dong Zhou,  Amir Bashan,  Yehiel Berezin,  Reuven Cohen,  Shlomo Havlin,  

pp.166-169

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.166

PDF download (339.5KB)

Cascading failures in interdependent networks have been investigated using percolation theory in recent years. Here, we study the dynamics of the cascading failures, the average and fluctuations of the total number of cascading, τ as a function of system size N near criticality. The system we analyzed is a pair of fully interdependent Erdös-Rényi (ER) networks. We show that when p is close to p_c, the whole dynamical process of cascading failures can be divided into three time stages. The giant component sizes in the second time stage, presented by a plateau in the size of giant component, have large standard deviations, which may not be well predicted by the mean-field theory. We also investigate the standard deviation of the total time std(τ) using simulations. When p = p_c, our numerical simulations indicate that std(τ) ∼ N^1/3, which increases faster than the mean which is predicted by the mean-field theory, < τ > ∼ N^1/4. We also find the scaling behavior as a function of N and p of < τ > and std(τ) for p < pc.

[1] J. Laprie, K. Kanoun, and M. Kaniche, “Modelling interdependencies between the electricity and information infrastructures,” Lect. Notes Comput. Sci. vol.4680, pp.54-67, 2007.

[2] V. Rosato, L. Issacharoff, F. Tiriticco, S. Meloni, S. De Porcellinis, and R. Setola, “Modelling interdependent infrastructures using interacting dynamical models,” Int. J. Crit. Infrastruct. vol.4, pp.63-79, 2008.

[3] S. Panzieri, and R. Setola, “Failures propagation in critical interdependent infrastructures,” Int. J. Model. Ident. Contr. vol.3, pp.69-78, 2008.

[4] A. Vespignani, “Complex networks: The fragility of interdependency,” Nature, vol.464, pp.984-985, 2010.

[5] S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, “Catastrophic cascade of failures in interdependent networks,” Nature, vol.464, pp.1025-1028, 2010.

[6] J. Gao, S. V. Buldyrev, H. E. Stanley, and S. Havlin, “Networks formed from interdependent networks,” Nat. Phys., vol.8, pp.40-48, 2011.

[7] E. A. Leicht, and R. M D'Souza, “Percolation on interacting networks,” preprint, arXiv:0907.0894.

[8] R. Parshani, S. V. Buldyrev, and S. Havlin, “Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition,” Phys. Rev. Lett., vol.105, 048701, 2010.

[9] J. Shao, S. V. Buldyrev, S. Havlin, and H. E. Stanley, “Cascade of failures in coupled network systems with multiple support-dependence relations,” Phys. Rev. E, vol.83, 036116, 2011.

[10] Y. Hu, B. Ksherim, R. Cohen, and S. Havlin, “Percolation in interdependent and interconnected networks: Abrupt change from second to first order transition,” Phys. Rev. E, vol.84, 066116, 2011.

[11] J. Gao, S. V. Buldyrev, S. Havlin, and H. E. Stanley, “Robustness of a network of networks,” Phys. Rev. Lett., vol.107, 195701, 2011.

[12] X. Huang, J. Gao, S. V. Buldyrev, S. Havlin, and H. E. Stanley, “Robustness of interdependent networks under targeted attack,” Phys. Rev. E, vol.83, 065101, 2011.

[13] G. Dong, J. Gao, L. Tian, R. Du, and Y. He, “Percolation of partially interdependent networks under targeted attack,” Phys. Rev. E, vol.85, 016112, 2012.

[14] W. Li, A. Bashan, S. V. Buldyrev, H. E. Stanley, and S. Havlin, “Cascading failures in interdependent lattice networks: The critical role of the length of dependency links,” Phys. Rev. Lett., vol.108, 228702, 2012.

[15] A. Bashan, Y. Berezin, S. V. Buldyrev, S. Havlin, “The extreme vulnerability of interdependent spatially embedded networks,” preprint, arXiv:1206.2062.