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arXiv · 1510.06487

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

Bernard Chazelle·Quansen Jiu·Qianxiao Li·Chu Wang
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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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Bernard Chazelle, Quansen Jiu, Qianxiao Li, Chu Wang. 2015-10-22. Well-Posedness of the Limiting Equation of a Noisy Consensus Model in Opinion Dynamics. https://arxiv.org/abs/1510.06487

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