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

被引：146

作者：

Duering, Bertram ^{[2
]}

Markowich, Peter ^{[1
,3
]}

Pietschmann, Jan-Frederik ^{[1
]}

Wolfram, Marie-Therese ^{[1
]}

机构：

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

[2] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[3] Univ Vienna, Fac Math, A-1090 Vienna, Austria

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2009年 / 465卷 / 2112期

关键词：

Boltzmann equation; Fokker-Planck equation; opinion formation; sociophysics; KINETIC APPROACH; CHOICE;

D O I：

10.1098/rspa.2009.0239

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：3687 / 3708

页数：22

共 22 条

[1]

[Anonymous], 2000, Sociodynamics: A Systematic Approach to Mathematical Modeling in the Social Sciences

[2]

[Anonymous], 2002, J ARTIF SOC SOC SIMU

[3] On a discrete generalized kinetic approach for modelling persuader's influence in opinion formation processes [J].

Bertotti, Maria Letizia ;

Delitala, Marcello .

MATHEMATICAL AND COMPUTER MODELLING, 2008, 48 (7-8) :1107-1121

[4] Boltzmann equations for mixtures of Maxwell gases: Exact solutions and power like tails [J].

Bobylev, A. V. ;

Gamba, I. M. .

JOURNAL OF STATISTICAL PHYSICS, 2006, 124 (2-4) :497-516

[5] A KINETIC APPROACH TO THE STUDY OF OPINION FORMATION [J].

Boudin, Laurent ;

Salvarani, Francesco .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2009, 43 (03) :507-522

[6] The social capital of opinion leaders [J].

Burt, RS .

ANNALS OF THE AMERICAN ACADEMY OF POLITICAL AND SOCIAL SCIENCE, 1999, 566 :37-54

[7]

Cercignani C., 1994, SPRINGER SERIES APPL, V106

[8] A BOLTZMANN-LIKE EQUATION FOR CHOICE FORMATION [J].

Comincioli, Valeriano ;

Della Croce, Lucia ;

Toscani, Giuseppe .

[9] Kinetic equations modelling wealth redistribution: A comparison of approaches [J].

Duering, Bertram ;

Matthes, Daniel ;

Toscani, Giuseppe .

PHYSICAL REVIEW E, 2008, 78 (05)

[10]

EGGER H, J NUMER ANA IN PRESS

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