Convergence analysis for asymmetric Deffuant-Weisbuch model

Jiangbo Zhang

Kybernetika (2014)

  • Volume: 50, Issue: 1, page 32-45
  • ISSN: 0023-5954

Abstract

top
In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation time with model parameters by simulations.

How to cite

top

Zhang, Jiangbo. "Convergence analysis for asymmetric Deffuant-Weisbuch model." Kybernetika 50.1 (2014): 32-45. <http://eudml.org/doc/261151>.

@article{Zhang2014,
abstract = {In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation time with model parameters by simulations.},
author = {Zhang, Jiangbo},
journal = {Kybernetika},
keywords = {opinion dynamics; asymmetric Deffuant–Weisbuch model; convergence; separation time; opinion dynamics; asymmetric Deffuant-Weisbuch model; convergence; separation time},
language = {eng},
number = {1},
pages = {32-45},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Convergence analysis for asymmetric Deffuant-Weisbuch model},
url = {http://eudml.org/doc/261151},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Zhang, Jiangbo
TI - Convergence analysis for asymmetric Deffuant-Weisbuch model
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 1
SP - 32
EP - 45
AB - In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation time with model parameters by simulations.
LA - eng
KW - opinion dynamics; asymmetric Deffuant–Weisbuch model; convergence; separation time; opinion dynamics; asymmetric Deffuant-Weisbuch model; convergence; separation time
UR - http://eudml.org/doc/261151
ER -

References

top
  1. Boyd, S., Ghosh, A., Prabhakar, B., Shah, D., 10.1109/TIT.2006.874516, Trans. Inform. Theory 52 (2006), 2508-2530. Zbl1283.94005MR2238556DOI10.1109/TIT.2006.874516
  2. Chow, Y., Teicher, H., Probability Theory: Independence Interchangeability Martingales. Second edition., Springer-Verlag, Heidelberg - Berlin 1978. MR0513230
  3. Deffuant, G., Neau, D., Amblard, F., Weisbuch, G., Mixing beliefs among interacting agents., Adv. in Complex Systems 3 (2000), 87-98. 
  4. Godsil, C., Royle, G., Algebraic Graph Theory., Springer-Verlag, New York 2001. Zbl0968.05002MR1829620
  5. Groeber, P., Schweitzer, F., Press, K., How groups can foster consensus: The case of local cultures., J. Artificial Societies and Social Simulations 12 (2009), 2/4. 
  6. Harary, F., A criterion for unanimity in French's theory of social power., In: Studies in Social Power, Ann Arbor 1959, pp. 168-182. 
  7. Hegselmann, R., Krause, U., Opinion dynamics and bounded confidence models. Analysis and Simulation., J. Artificial Societies and Social Simulations 5 (2002), 3. 
  8. Hong, Y., Gao, L., Cheng, D., Hu, J., 10.1109/TAC.2007.895860, IEEE Trans. Automat. Control 52 (2007), 943-948. MR2324260DOI10.1109/TAC.2007.895860
  9. Hu, J., On robust consensus of multi-agent systems with communication delays., Kybernetika 45 (2009), 768-784. Zbl1190.93003MR2599111
  10. Jiang, L., Hua, D., Zhu, J., Wang, B., Zhou., T., 10.1140/epjb/e2008-00342-3, The European Physical Journal B 65 (2008), 2, 251-255. DOI10.1140/epjb/e2008-00342-3
  11. Lorenz, J., 10.1142/S0129183107011789, Internat. J. of Modern Physics C 18 (2007), 12, 1819-1838. Zbl1151.91076DOI10.1142/S0129183107011789
  12. Lou, Y., Hong, Y., 10.1016/j.automatica.2012.02.032, Automatica 48 (2012), 5, 879-885. Zbl1246.93104MR2912813DOI10.1016/j.automatica.2012.02.032
  13. Serge, M., Marisa, Z., 10.1037/h0027568, J. Personal. Soc. Psychology 12 (1969), 1, 125-135. DOI10.1037/h0027568
  14. Shi, G., Hong, Y., 10.1016/j.automatica.2008.12.015, Automatica 45 (2009), 1165-1175. Zbl1162.93308MR2531590DOI10.1016/j.automatica.2008.12.015
  15. Thunberg, J., Song, W., Hong, Y., Hu, X., Distributed attitude synchronization using backstepping and sliding mode control., Journal of Control Theory and Applications 12 (2014), 1, 48-55. MR3152182
  16. Touri, B., Product of Random Stochastic Matrices And Distributed Averaging., Ph.D. Thesis, Dept. of Industrial Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2011. Zbl1244.15023
  17. Weisbuch, G., Deffuant, G., Amblard, F., Nadal, J., 10.1002/cplx.10031, Complexity 7 (2002), 3, 55-63. DOI10.1002/cplx.10031
  18. Zhang, J., Hong, Y., 10.1016/j.physa.2013.07.014, Physica A 392 (2013), 5289-5297. MR3102806DOI10.1016/j.physa.2013.07.014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.