ANALYSIS OF MEAN-FIELD APPROXIMATION FOR DEFFUANT OPINION DYNAMICS ON NETWORKS

Research output: Contribution to journalArticlepeer-review

Abstract

Mean-field equations have been developed recently to approximate the dynamics of the Deffuant model of opinion formation. These equations can describe both fully mixed populations and the case where individuals interact only along edges of a network. In each case, interactions only occur between individuals whose opinions differ by less than a given parameter, called the confidence bound. The size of the confidence bound parameter is known to strongly affect both the dynamics and the number and location of opinion clusters. In this work, we carry out a mathematical analysis of the mean-field equations to investigate the role of the confidence bound and boundaries on these important observables of the model. We consider the limit in which the confidence bound interval is small, and we identify the key mechanisms driving opinion evolution. We show that linear stability analysis can predict the number and location of opinion clusters. Comparison with numerical simulations of the model illustrates that the early-time dynamics and the final cluster locations can be accurately approximated for networks composed of two degree classes, as well as for the case of a fully mixed population.

Original languageEnglish
Pages (from-to)436-459
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume83
Issue number2
DOIs
Publication statusPublished - 2023

Keywords

  • asymptotic analysis
  • cluster formation
  • linear stability
  • mean-field approximation
  • opinion dynamics
  • social networks

Fingerprint

Dive into the research topics of 'ANALYSIS OF MEAN-FIELD APPROXIMATION FOR DEFFUANT OPINION DYNAMICS ON NETWORKS'. Together they form a unique fingerprint.

Cite this