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arXiv · 2005.08030

Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay

Alessandro Paolucci
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Abstract

In this paper we study a Hegselmann-Krause opinion formation model with distributed time delay and positive influence functions. Through a Lyapunov functional approach, we provide a consensus result under a smallness assumption on the initial delay. Furthermore, we analyze a transport equation, obtained as mean--field limit of the particle one. We prove global existence and uniqueness of the measure-valued solution for the delayed transport equation and its convergence to consensus under a smallness assumption on the delay, using a priori estimates which are uniform with respect to the number of agents.

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Alessandro Paolucci. 2020-05-16. Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay. https://arxiv.org/abs/2005.08030

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