Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay
Analysis of PDEs
2020-05-19 v1
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.
Cite
@article{arxiv.2005.08030,
title = {Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay},
author = {Alessandro Paolucci},
journal= {arXiv preprint arXiv:2005.08030},
year = {2020}
}