Boltzmann and Fokker-Planck Equations Modelling Opinion Formation in the Presence of Strong Leaders

20 Pages Posted: 5 May 2009

See all articles by Bertram Düring

Bertram Düring

University of Warwick - Mathematics Institute

Peter A. Markowich

University of Cambridge

Jan-Frederik Pietschmann

University of Cambridge

Marie-Therese Wolfram

University of Cambridge

Date Written: May 4, 2009

Abstract

We propose a mathematical model for opinion formation in a society which 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 (2006) 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 which 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.

Keywords: Boltzmann equation, Fokker-Planck equation, opinion formation, sociophysics

Suggested Citation

Düring, Bertram and Markowich, Peter A. and Pietschmann, Jan-Frederik and Wolfram, Marie-Therese, Boltzmann and Fokker-Planck Equations Modelling Opinion Formation in the Presence of Strong Leaders (May 4, 2009). Available at SSRN: https://ssrn.com/abstract=1399345 or http://dx.doi.org/10.2139/ssrn.1399345

Bertram Düring (Contact Author)

University of Warwick - Mathematics Institute ( email )

Zeeman Building
Coventry, CV4 7AL
United Kingdom

Peter A. Markowich

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

Jan-Frederik Pietschmann

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

Marie-Therese Wolfram

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

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