Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders

Bertram Düring, Peter Markowich*, Jan Frederik Pietschmann, Marie Therese Wolfram

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

112 Scopus citations


We propose a mathematical model for opinion formation in a society that is built of two groups, one group of 'ordinary' people and one group of 'strong opinion leaders'. Our approach is based on an opinion formation model introduced in Toscani (Toscani 2006 Commun. Math. Sci. 4, 481-496) and borrows ideas from the kinetic theory of mixtures of rarefied gases. Starting from microscopic interactions among individuals, we arrive at a macroscopic description of the opinion formation process that is characterized by a system of Fokker-Planck-type equations. We discuss the steady states of this system, extend it to incorporate emergence and decline of opinion leaders and present numerical results.

Original languageEnglish (US)
Pages (from-to)3687-3708
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2112
StatePublished - Dec 8 2009


  • Boltzmann equation
  • Fokker-Planck equation
  • Opinion formation
  • Sociophysics

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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