Abstract and Applied Analysis

Dynamics of an Information Spreading Model with Isolation

Xia-Xia Zhao and Jian-Zhong Wang

Full-text: Access has been disabled (more information)

Abstract

Information plays an important role in modern society. In this paper, we presented a mathematical model of information spreading with isolation. It was found that such a model has rich dynamics including Hopf bifurcation. The results showed that, for a wide range of parameters, there is a bistable phenomenon in the process of information spreading and thus the information cannot be well controlled. Moreover, the model has a limit cycle which implies that the information exhibits periodic outbreak which is consistent with the observations in the real world.

Article information

Source
Abstr. Appl. Anal. Volume 2014, Special Issue (2014), Article ID 484630, 6 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
http://projecteuclid.org/euclid.aaa/1425048251

Digital Object Identifier
doi:10.1155/2014/484630

Citation

Zhao, Xia-Xia; Wang, Jian-Zhong. Dynamics of an Information Spreading Model with Isolation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 484630, 6 pages. doi:10.1155/2014/484630. http://projecteuclid.org/euclid.aaa/1425048251.


Export citation

References

  • 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.
  • Y. Moreno, M. Nekovee, and A. F. Pacheco, “Dynamics of rumor spreading in complex networks,” Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, vol. 69, no. 6, Article ID 066130, p. 1, 2004.
  • D. J. Daley and D. G. Kendall, “Epidemics and Rumours,” Nature, vol. 204, no. 4963, article 1118, 1964.
  • D. H. Zanette, “Critical behavior of propagation on small-world networks,” Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, vol. 64, no. 5, Article ID 050901, 2001.
  • L. Lü, D.-B. Chen, and T. Zhou, “The small world yields the most effective information spreading,” New Journal of Physics, vol. 13, Article ID 123005, 2011.
  • A. L. Hill, D. G. Rand, M. A. Nowak, and N. A. Christakis, “Infectious disease modeling of social contagion in networks,” PLoS Computational Biology, vol. 6, no. 11, Article ID e1000968, 2010.
    Mathematical Reviews (MathSciNet): MR2754025
    Digital Object Identifier: doi:10.1371/journal.pcbi.1000968
  • T. House, “Modelling behavioural contagion,” Journal of the Royal Society Interface, vol. 8, no. 59, pp. 909–912, 2011.
  • Z.-Q. Zhu, C.-J. Liu, J.-L. Wu, J. Xu, and B. Liu, “The influence of human heterogeneity to information spreading,” Journal of Statistical Physics, vol. 154, no. 6, pp. 1569–1577, 2014.
    Mathematical Reviews (MathSciNet): MR3176420
  • čommentComment on ref. [9?]: Please note that the URL is not accessible.http://www.iyaxin.com/content/2008-10/21/content_450073.htm.
    URL: Link to item
  • J. Leskovec, M. McGlohon, C. Faloutsos, N. Glance, and M. Hurst, “Patterns of cascading behavior in large blog graphs,” in Proceedings of the 7th SIAM International Conference on Data Mining, pp. 551–556, April 2007.
  • D. Gruhl, D. Liben-Nowell, R. Guha, and A. Tomkins, “Information diffusion through blogspace,” in Proceedings of the 13th International World Wide Web Conference Proceedings (WWW '04), pp. 491–501, May 2004.
  • R. Narayanam and Y. Narahari, “A shapley value-based approach to discover influential nodes in social networks,” IEEE Transactions on Automation Science and Engineering, vol. 8, no. 1, pp. 130–147, 2011.
  • M. Lahiri and M. Cebrian, “The genetic algorithm as a general diffusion model for social networks,” in Proceedings of the 24th AAAI Conference on Artificial Intelligence, pp. 494–499, July 2010.
  • B. Suh, L. Hong, P. Pirolli, and E. H. Chi, “Want to be retweeted? Large scale analytics on factors impacting retweet in twitter network,” in Proceedings of the 2nd IEEE International Conference on Social Computing (SocialCom '10), pp. 177–184, August 2010.
  • J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42, Springer, New York, NY, USA, 1990.
    Mathematical Reviews (MathSciNet): MR1139515
  • J. Arino, C. C. McCluskey, and P. van den Driessche, “Global results for an epidemic model with vaccination that exhibits backward bifurcation,” SIAM Journal on Applied Mathematics, vol. 64, no. 1, pp. 260–276, 2003.
    Mathematical Reviews (MathSciNet): MR2029134
    Zentralblatt MATH: 1034.92025
    Digital Object Identifier: doi:10.1137/S0036139902413829
  • J. Dushoff, W. Huang, and C. Castillo-Chavez, “Backwards bifurcations and catastrophe in simple models of fatal diseases,” Journal of Mathematical Biology, vol. 36, no. 3, pp. 227–248, 1998.
    Mathematical Reviews (MathSciNet): MR1608613
    Zentralblatt MATH: 0917.92022
    Digital Object Identifier: doi:10.1007/s002850050099
  • L. Perko, Differential Equations and Dynamical Systems, vol. 7, Springer, New York, NY, USA, 2nd edition, 1996.
    Mathematical Reviews (MathSciNet): MR1418638
  • Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, vol. 112, Springer, New York, NY, USA, 1995.
    Mathematical Reviews (MathSciNet): MR1344214
  • J. V. Carlis and J. A. Konstan, “Interactive visualization of serial periodic data,” in Proceedings of the 11th Annual ACM Symposium on User Interface Software and Technology (UIST '98), pp. 29–38, November 1998.
  • M. Yang, G. Chen, and X. Fu, “A modified SIS model with an infective medium on complex networks and its global stability,” Physica A. Statistical Mechanics and its Applications, vol. 390, no. 12, pp. 2408–2413, 2011.
  • A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999.
    Mathematical Reviews (MathSciNet): MR2091634
    Zentralblatt MATH: 1226.05223
    Digital Object Identifier: doi:10.1126/science.286.5439.509
  • A.-L. Barabási, R. Albert, and H. Jeong, “Mean-field theory for scale-free random networks,” Physica A. Statistical Mechanics and its Applications, vol. 272, no. 1, pp. 173–187, 1999.
  • R. Pastor-Satorras and A. Vespignani, “Epidemic spreading in scale-free networks,” Physical Review Letters, vol. 86, no. 14, pp. 3200–3203, 2001. \endinput

Hindawi

Abstract and Applied Analysis

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more