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

Bertram Düring; Peter Markowich; Jan Frederik Pietschmann; Marie Therese Wolfram

doi:10.1098/rspa.2009.0239

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 journal › Article › peer-review

154 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	3687-3708
Number of pages	22
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	465
Issue number	2112
DOIs	https://doi.org/10.1098/rspa.2009.0239
State	Published - Dec 8 2009
Externally published	Yes

Keywords

Boltzmann equation
Fokker-Planck equation
Opinion formation
Sociophysics

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rspa.2009.0239

Cite this

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title = "Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders",

abstract = "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.",

keywords = "Boltzmann equation, Fokker-Planck equation, Opinion formation, Sociophysics",

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year = "2009",

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doi = "10.1098/rspa.2009.0239",

language = "English (US)",

volume = "465",

pages = "3687--3708",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

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Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. / Düring, Bertram; Markowich, Peter; Pietschmann, Jan Frederik et al.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 465, No. 2112, 08.12.2009, p. 3687-3708.

Research output: Contribution to journal › Article › peer-review

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T1 - Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders

AU - Düring, Bertram

AU - Markowich, Peter

AU - Pietschmann, Jan Frederik

AU - Wolfram, Marie Therese

PY - 2009/12/8

Y1 - 2009/12/8

N2 - 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.

AB - 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.

KW - Boltzmann equation

KW - Fokker-Planck equation

KW - Opinion formation

KW - Sociophysics

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SN - 1364-5021

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

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Keywords

ASJC Scopus subject areas

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