Skip to main content
Log in

Load-induced cascading failures in interconnected networks

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Recently, the robustness of coupled network under cascading failure has attracted a lot of attention. In this paper, we concentrate on the interconnected network, which is a typical coupled network in the real world. Considering the coupling effects, the cascading model of interconnected network was built. By adjusting the contribution of intra-links and interlinks to the loads, we find that interconnected network is more robust if the interlinks contribute more to the loads. We also investigate the influence of coupling and intra-layer node-linking similarity in the robustness of interconnected network under intentional attack; through numerical simulations, we find that compared with random homogeneous distribution, the robustness of interconnected network can be greatly enhanced with heterogeneous inter-degree distribution if to be designed positively related to intra-degree, but when the average inter-degree gets a certain value, interconnected network is most vulnerable to cascading failures. We also find that contrary to what isolated network behaves, interconnected network is more robust with larger intra-layer disassortativity. Our work may be helpful for designing high robust interconnected network or improving the robustness of interconnected network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwanga, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)

    Article  MathSciNet  Google Scholar 

  2. Motter, A.E., Lai, Y.C.: Cascade-based attacks on complex networks. Phys. Rev. E 66, 065102 (2002)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Motter, A.E.: Cascade control and defense in complex networks. Phys. Rev. Lett. 93, 098701 (2004)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Wang, J.W., Rong, L.L.: A model for cascading failures in scale-free networks with a breakdown probability. Phys. A 388, 1289–1298 (2009)

    Article  Google Scholar 

  8. Zhang, J.F., Yang, L.X., Gao, Z.Y.: Cascading failure in congested scale-free networks. Int. J. Mod. Phys. C 21, 991–999 (2010)

    Article  Google Scholar 

  9. Wei, D.Q., Luo, X.S., Zhang, B.: Analysis of cascading failure in complex power networks under the load local preferential redistribution rule. Phys. A 391, 2771–2777 (2012)

    Article  Google Scholar 

  10. 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 

  11. 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, 048701 (2010)

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

    Article  MathSciNet  Google Scholar 

  13. 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, 065101 (2011)

    Article  Google Scholar 

  14. Buldyrev, S.V., Shere, N.W., Cwilich, G.A.: Interdependent networks with identical degrees of mutually dependent nodes. Phys. Rev. E 83, 016112 (2011)

    Article  MathSciNet  Google Scholar 

  15. Zhou, D., Gao, J.X., Havlin, S., Stanley, H.E.: Percolation of partially interdependent scale-free networks. Phys. Rev. E 87, 052812 (2013)

    Article  Google Scholar 

  16. Zhou, D., Stanley, H.E., D’Agostino, G., Scala, A.: Assortativity decreases the robustness of interdependent networks. Phys. Rev. E 86, 066103 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Shao, S., Huang, X.Q., Stanley, H.E., Havlin, S.: Robustness of partially interdependent network formed of clustered networks. Phys. Rev. E 89, 032812 (2014)

    Article  Google Scholar 

  19. Zio, E., Sansavini, G.: Modeling interdependent network systems for identifying cascade-safe operating margins. IEEE. Trans. Reliab. 60, 94–101 (2011)

    Article  Google Scholar 

  20. Brummitt, C.D., D’Souza, R.M., Leicht, E.A.: Suppressing cascades of load in interdependent networks. PNAS 109, E680–E689 (2012)

    Article  Google Scholar 

  21. Tan, F., Xia, Y.X., Zhang, W.P., Jin, X.Y.: Cascading failures of loads in interconnected networks under intentional attack. EPL 102, 28009 (2013)

    Article  Google Scholar 

  22. Qiu, Y.Z.: Optimal weighting scheme and the role of coupling strength against load failures in degree-based weighted interdependent networks. Phys. A 392, 1920–1924 (2013)

    Article  Google Scholar 

  23. Goh, K.I., Kahng, B., Kim, D.: Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87, 278701 (2001)

    Article  Google Scholar 

  24. Barthélemy, M.: Betweenness centrality in large complex networks. Eur. Phys. J. B 38, 163–168 (2004)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  26. Newman, M.E.J.: The structure and function of complex networks. Phys. Rev. Lett. 89, 208701 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Shaanxi Science Foundation of China (Grant No. 2012JM8035).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xingzhao Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, X., Yao, H., Du, J. et al. Load-induced cascading failures in interconnected networks. Nonlinear Dyn 82, 97–105 (2015). https://doi.org/10.1007/s11071-015-2141-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2141-y

Keywords

Navigation