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

Bernard Chazelle; Quansen Jiu; Qianxiao Li; Chu Wang

doi:10.1016/j.jde.2017.02.036

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

Bernard Chazelle, Quansen Jiu, Qianxiao Li, Chu Wang

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

20 Scopus citations

Abstract

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 multiagent system for opinion dynamics. 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.

Original language	English (US)
Pages (from-to)	365-397
Number of pages	33
Journal	Journal of Differential Equations
Volume	263
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2017.02.036
State	Published - Jul 5 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Global stability
Hegselmann–Krause model
Nonlinear Fokker–Planck equation
Well-posedness

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10.1016/j.jde.2017.02.036

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title = "Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics",

abstract = "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 multiagent system for opinion dynamics. 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.",

keywords = "Global stability, Hegselmann–Krause model, Nonlinear Fokker–Planck equation, Well-posedness",

author = "Bernard Chazelle and Quansen Jiu and Qianxiao Li and Chu Wang",

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AU - Chazelle, Bernard

AU - Jiu, Quansen

AU - Li, Qianxiao

AU - Wang, Chu

PY - 2017/7/5

Y1 - 2017/7/5

N2 - 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 multiagent system for opinion dynamics. 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.

AB - 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 multiagent system for opinion dynamics. 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.

KW - Global stability

KW - Hegselmann–Krause model

KW - Nonlinear Fokker–Planck equation

KW - Well-posedness

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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