Well-Posedness of the Limiting Equation of a Noisy Consensus Model in Opinion Dynamics

2015/10/22 by Bernard Chazelle, Chazelle, Bernard, Quansen Jiu +5 · 5 citations
Physics and Astronomy · #35Q70 #35Q91 #Analysis of PDEs (math.AP) #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.1510.06487

openalex publication_date 2015/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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