Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 453689, 13 pages
http://dx.doi.org/10.1155/2013/453689
Research Article

Cascading Dynamics of Heterogenous Scale-Free Networks with Recovery Mechanism

1College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, Shandong 264005, China
2School of Computer Science, National University of Defense Technology, Changsha, Hunan 410073, China
3Shandong Provincial Key Laboratory of Network Based Intelligent Computing, University of Jinan, Jinan 250022, China
4Information Security Center, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876, China
5National Computer Network Emergency Response Technical Team/Coordination Center, Beijing 100029, China

Received 11 November 2013; Accepted 6 December 2013

Academic Editor: Shuping He

Copyright © 2013 Shudong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Albert, H. Jeong, and A.-L. Barabási, “Error and attack tolerance of complex networks,” Nature, vol. 406, pp. 378–382, 2000. View at Google Scholar
  2. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Network robustness and fragility: percolation on random graphs,” Physical Review Letters, vol. 85, no. 25, pp. 5468–5471, 2000. View at Publisher · View at Google Scholar
  3. A. E. Motter, “Cascade control and defense in complex networks,” Physical Review Letters, vol. 93, no. 9, Article ID 098701, 2004. View at Publisher · View at Google Scholar
  4. A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Physical Review E, vol. 66, no. 6, Article ID 065102, 4 pages, 2002. View at Publisher · View at Google Scholar
  5. R. Pastor-Satorras, A. Vázquez, and A. Vespignani, “Dynamical and correlation properties of the internet,” Physical Review Letters, vol. 87, no. 25, Article ID 258701, 4 pages, 2001. View at Publisher · View at Google Scholar
  6. V. Rosato, L. Issacharoff, F. Tiriticco, S. Meloni, S. de Porcellinis, and R. Setola, “Modelling interdependent infrastructures using interacting dynamical models,” International Journal of Critical Infrastructures, vol. 4, no. 1-2, pp. 63–79, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Santiago and R. M. Benito, “Robustness of heterogeneous complex networks,” Physica A, vol. 388, no. 11, pp. 2234–2242, 2009. View at Google Scholar
  8. Y. X. Xia and D. J. Hill, “Attack vulnerability of complex communication networks,” IEEE Transactions on Circuits and Systems II, vol. 55, no. 1, pp. 65–69, 2008. View at Google Scholar
  9. P. Holme, B. J. Kim, C. N. Yoon, and S. K. Han, “Attack vulnerability of complex networks,” Physical Review E, vol. 65, no. 5, Article ID 056109, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, “Catastrophic cascade of failures in interdependent networks,” Nature, vol. 464, no. 7291, pp. 1025–1028, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. S. V. Buldyrev, N. W. Shere, and G. A. Cwilich, “Interdependent networks with identical degrees of mutually dependent nodes,” Physical Review E, vol. 83, no. 1, Article ID 016112, 8 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  12. I. Simonsen, L. Buzna, K. Peters, S. Bornholdt, and D. Helbing, “Transient dynamics increasing network vulnerability to cascading failures,” Physical Review Letters, vol. 100, no. 21, Article ID 218701, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. A. E. Motter, “Cascade control and defense in complex networks,” Physical Review Letters, vol. 93, no. 9, Article ID 098701, 4 pages, 2004. View at Publisher · View at Google Scholar
  14. L. K. Gallos, R. Cohen, P. Argyrakis, A. Bunde, and S. Havlin, “Stability and topology of scale-free networks under attack and defense strategies,” Physical Review Letters, vol. 94, no. 18, Article ID 188701, 2005. View at Publisher · View at Google Scholar
  15. L. Buzna, K. Peters, H. Ammoser, C. Kühnert, and D. Helbing, “Efficient response to cascading disaster spreading,” Physical Review E, vol. 75, no. 5, Article ID 056107, 7 pages, 2007. View at Publisher · View at Google Scholar
  16. B. A. Rezaei, N. Sarshar, V. P. Roychowdhury, and P. O. Boykin, “Disaster management in power-law networks: recovery from and protection against intentional attacks,” Physica A, vol. 381, no. 1-2, pp. 497–514, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Peters, L. Buzna, and D. Helbing, “Modelling of cascading effects and efficient response to disaster spreading in complex networks,” International Journal of Critical Infrastructures, vol. 4, no. 1-2, pp. 46–62, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Yang, W.-X. Wang, Y.-C. Lai, and G.-R. Chen, “Optimal weighting scheme for suppressing cascades and traffic congestion in complex networks,” Physical Review E, vol. 79, no. 2, Article ID 026112, 2009. View at Publisher · View at Google Scholar
  19. B.-L. Dou, X.-G. Wang, and S.-Y. Zhang, “Robustness of networks against cascading failures,” Physica A, vol. 389, no. 11, pp. 2310–2317, 2010. View at Google Scholar
  20. J. Domingo-Ferrer and U. González-Nicolás, “Decapitation of networks with and without weights and direction: the economics of iterated attack and defense,” Computer Networks, vol. 5, no. 1, pp. 119–130, 2011. View at Google Scholar
  21. M. Ouyang, L. Hong, Z.-J. Mao, M.-H. Yu, and F. Qi, “A methodological approach to analyze vulnerability of interdependent infrastructures,” Simulation Modelling Practice and Theory, vol. 17, pp. 817–828, 2009. View at Google Scholar
  22. I. Mishkovski, M. Biey, and L. Kocarev, “Vulnerability of complex networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 341–349, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. E. Bompard, D. Wu, and F. Xue, “Structural vulnerability of power systems: a topological approach,” Electric Power Systems Research, vol. 81, no. 7, pp. 1334–1340, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Babaei, H. Ghassemieh, and M. Jalili, “Cascading failure tolerance of modular small-world networks,” IEEE Transactions on Circuits and Systems II, vol. 58, no. 8, pp. 527–531, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. J.-W. Wang and L. Rong, “Robustness of the western United States power grid under edge attack strategies due to cascading failures,” Safety Science, vol. 49, pp. 807–812, 2011. View at Google Scholar
  26. H. Ren and I. Dobson, “Using transmission line outage data to estimate cascading failure propagation in an electric power system,” IEEE Transactions on Circuits and Systems Part II, vol. 55, no. 9, pp. 927–931, 2008. View at Google Scholar
  27. B. K. Mishra and A. K. Singh, “Two quarantine models on the attack of malicious objects in computer network,” Mathematical Problems in Engineering, vol. 2012, Article ID 407064, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. M.-G. Hua, P. Cheng, J.-T. Fei, J.-Y. Zhang, and J.-F. Chen, “Network-based robust H filtering for the uncertain systems with sensor failures and noise disturbance,” Mathematical Problems in Engineering, vol. 2012, Article ID 945271, 19 pages, 2012. View at Publisher · View at Google Scholar
  29. M. Li and W. Zhao, “On 1/f noise,” Mathematical Problems in Engineering, vol. 2012, Article ID 673648, 23 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. M. Li and W. Zhao, “Visiting power laws in cyber-physical networking systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 302786, 13 pages, 2012. View at Publisher · View at Google Scholar
  32. R. Parshani, S. V. Buldyrev, and S. Havlin, “Critical effect of dependency groups on the function of networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 108, no. 3, pp. 1007–1010, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. J.-X. Gao, S. V. Buldyrev, H. E. Stanley, and S. Havlin, “Networks formed from interdependent networks,” Nature Physics, vol. 8, no. 1, pp. 40–48, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. X. Q. Huang, J. Gao, S. V. Buldyrev, S. Havlin, and H. E. Stanley, “Robustness of interdependent networks under targeted attack,” Physical Review E, vol. 83, no. 6, Article ID 065101, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. W. Li, A. Bashan, S. V. Buldyrev et al., “Cascading failures in interdependent lattice networks: the critical role of the length of dependency links,” Physical Review Letters, vol. 108, Article ID 228702, 2012. View at Google Scholar
  36. M. Li and W. Zhao, “Representation of a stochastic traffic bound,” IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 9, pp. 1368–1372, 2010. View at Publisher · View at Google Scholar · View at Scopus
  37. M. Li, W. Zhao, and C. Cattani, “Delay bound: fractal traffic passes through servers,” Mathematical Problems in Engineering, vol. 2013, Article ID 157636, 15 pages, 2013. View at Publisher · View at Google Scholar
  38. S. He, Z. Ding, and F. Liu, “Output regulation of a class of continuous-time Markovian jumping systems,” Signal Processing, vol. 93, no. 2, pp. 411–419, 2013. View at Google Scholar
  39. S. He and F. Liu, “Finite-time H control of nonlinear jump systems with time-delays via dynamic observer-based state feedback,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 605–614, 2012. View at Google Scholar
  40. A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Physical Review E, vol. 66, no. 6, Article ID 065102, 2002. View at Publisher · View at Google Scholar · View at Scopus
  41. F. Holme and B. J. Kim, “Vertex overload breakdown in evolving networks,” Physical Review E, vol. 65, no. 6, Article ID 066109, 2002. View at Publisher · View at Google Scholar · View at Scopus
  42. P. Crucitti, V. Latora, and M. Marchiori, “Model for cascading failures in complex networks,” Physical Review E, vol. 69, Article ID 045104, 4 pages, 2004. View at Publisher · View at Google Scholar
  43. R. Kinney, P. Crucitti, R. Albert, and V. Latora, “Modeling cascading failures in the North American power grid,” European Physical Journal B, vol. 46, no. 1, pp. 101–107, 2005. View at Publisher · View at Google Scholar · View at Scopus
  44. D. Heide, M. Schafer, and M. Greiner, “Robustness of networks against fluctuation-induced cascading failures,” Physical Review E, vol. 77, no. 5, Article ID 056103, 2008. View at Publisher · View at Google Scholar
  45. W.-X. Wang and G.-R. Chen, “Universal robustness characteristic of weighted networks against cascading failure,” Physical Review E, vol. 77, no. 2, Article ID 026101, 2008. View at Publisher · View at Google Scholar
  46. B. Mirzasoleiman, M. Babaei, M. Jalili, and M. Safari, “Cascaded failures in weighted networks,” Physical Review E, vol. 84, no. 4, Article ID 046114, 2011. View at Publisher · View at Google Scholar · View at Scopus
  47. J.-W. Wang and L.-L. Rong, “A model for cascading failures in scale-free networks with a breakdown probability,” Physica A, vol. 388, no. 7, pp. 1289–1298, 2009. View at Publisher · View at Google Scholar · View at Scopus
  48. S. J. Qin, Y. Chen, and M. Yang, “A edge-based-attack robust model of capacity for cascading failures,” in Proceedings of the IEEE International Conference on Advanced Computer Control (ICACC '10), pp. 136–139, March 2010. View at Publisher · View at Google Scholar · View at Scopus
  49. W.-X. Wang and Y.-C. Lai, “Abnormal cascading on complex networks,” Physical Review E, vol. 80, no. 3, Article ID 036109, 2009. View at Publisher · View at Google Scholar
  50. A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” American Association for the Advancement of Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  51. J. Leskovec, J. Kleinberg, and C. Faloutsos, “Graphs over time: densification laws, shrinking diameters and possible explanations,” in Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 177–187, Chicago, Ill, USA, August 2005. View at Publisher · View at Google Scholar · View at Scopus
  52. M. Girvan and M. E. J. Newman, “Community structure in social and biological networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 12, pp. 7821–7826, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  53. T. B. Hashimoto, M. Nagasaki, K. Kojima, and S. Miyano, “BFL: a node and edge betweenness based fast layout algorithm for large scale networks,” BMC Bioinformatics, vol. 10, article 19, 2009. View at Publisher · View at Google Scholar · View at Scopus
  54. M. Ercsey-Ravasz and Z. Toroczkai, “Centrality scaling in large networks,” Physical Review Letters, vol. 105, no. 3, Article ID 038701, 2010. View at Publisher · View at Google Scholar · View at Scopus