Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Chazelle, Bernard¹  Jiu, Quansen³  Li, Qianxiao²  Wang, Chu^2,4 

[1] Princeton Univ, Dept Comp Sci, Princeton, NJ 08540 USA

[2] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08540 USA

[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[4] Nokia Bell Labs, 600-700 Mt Ave, Murray Hill, NJ 07974 USA

关键词: Hegselmann-Krause model;    Nonlinear Fokker-Planck equation;    Well-posedness;    Global stability;   

DOI  :  10.1016/j.jde.2017.02.036

来源: Elsevier

【 摘 要 】

This paper establishes the global well-posedness of the nonlinear Fokker-Planck equation for a noisy version of the Hegselmann-Krause model. The equation captures the mean-field behavior of a classic multi agent system for opinion dyrignics. We prove the global existence, uniqueness, nonnegativity and regularity of the weak solution. We also exhibit a global stability condition, which delineates a forbidden region for consensus formation. This is the first nonlinear stability result derived for the Hegselmann-Krause model. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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