Geodesic
Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay
Minimax theory and its applications, Tome 6 (2021) no. 2
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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 themeasure-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.
Mots-clés : Hegselmann-Krause model, opinion formation, delay, consensus 
@article{MTA_2021_6_2_a13,
     author = {Alessandro Paolucci},
     title = {Convergence to consensus for a {Hegselmann-Krause-type} model with distributed time delay},
     journal = {Minimax theory and its applications},
     year = {2021},
     volume = {6},
     number = {2},
     zbl = {1471.34156},
     url = {http://geodesic.mathdoc.fr/item/MTA_2021_6_2_a13/}
}
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AU  - Alessandro Paolucci
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JO  - Minimax theory and its applications
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IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MTA_2021_6_2_a13/
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%N 2
%U http://geodesic.mathdoc.fr/item/MTA_2021_6_2_a13/
%F MTA_2021_6_2_a13
Alessandro Paolucci. Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay. Minimax theory and its applications, Tome 6 (2021) no. 2. http://geodesic.mathdoc.fr/item/MTA_2021_6_2_a13/