Skip to main content

Collective Phenomena in Complex Social Networks

  • Chapter
Applications of Nonlinear Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

  • 2150 Accesses

Abstract

The problem of social consensus is approached from the perspective of nonlinear dynamics of interacting agents in a complex network. Some basic concepts, such as dynamical metastability, are discussed in the framework of the prototype voter model. In the context of Axelrod’s model for the dissemination of culture we describe a co-evolutionary dynamics formulation with recent results on group formation and nonequilibrium network fragmentation and recombination transitions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Holley R. Liggett T., Ann. Probab. 4, 1975, 195.

    Article  MathSciNet  Google Scholar 

  2. T.M. Liggett, Interacting Particle Systems (Springer, New York 1985).

    MATH  Google Scholar 

  3. R. Axelrod, The dissemination of culture: A model with local convergence and global polarization, J. Conflict Res. 41, 203–226 (1997).

    Article  Google Scholar 

  4. I. Dornic, H. Chaté, J. Chavé, and H. Hinrichsen, Critical Coarsening without Surface Tension: The Universality Class of the Voter Model, Phys. Rev. Lett. 87, 045701–045074 (2001).

    Article  Google Scholar 

  5. C. Castellano, D. Vilone, and A. Vespignani, Incomplete ordering of the voter model on small-world networks, Europhy. Lett. 63, 153–158 (2003).

    Article  Google Scholar 

  6. K. Suchecki, V.M. Eguíluz, and M. San Miguel, Conservation laws for the voter model in complex networks, Europhy. Lett. 69, 228–234 (2005).

    Article  Google Scholar 

  7. V. Sood and S. Redner, Voter Model on Heterogeneous Graphs, Phys. Rev. Lett. 94, 178701–178704 (2005).

    Article  Google Scholar 

  8. K. Suchecki, V.M. Eguíluz, and M. San Miguel, Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution, Phys. Rev. E (2005).

    Google Scholar 

  9. L. Frachebourg and P.L. Krapivsky, Exact results for kinetics of catalytic reactions, Phys. Rev. E 53, R3009–3012 (1996).

    Article  Google Scholar 

  10. D.J. Watts and S.H. Strogatz, Collective dynamics of ‘small-world’ networks, Nature 393, 440–443 (1998).

    Article  Google Scholar 

  11. P.L. Krapivsky, Kinetics of monomer-monomer surface catalytic reactions, Phys. Rev. A 45, 1067–1072 (1992).

    Article  Google Scholar 

  12. A.L. Barabási and R. Albert, Emergence of Scaling in Random Networks, Science 286, 509–512 (1999).

    Article  MathSciNet  Google Scholar 

  13. F. Vazquez, J.C. Gonzalez-Avella, V. M. Eguiluz and M. San Miguel, Phys. Rev. E (2007), arXiv:0708.0776.

    Google Scholar 

  14. D. Centola, J.C. Gonzalez-Avella, V. M. Eguiluz, and M. San Miguel, J. Conflict Resolution (2007).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Vazquez, F., González-Avella, J.C., Eguíluz, V.M., Miguel, M.S. (2009). Collective Phenomena in Complex Social Networks. In: In, V., Longhini, P., Palacios, A. (eds) Applications of Nonlinear Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85632-0_15

Download citation

Publish with us

Policies and ethics