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Minimax Theory and its Applications 06 (2021), No. 2, 379--394
Copyright Heldermann Verlag 2021



Convergence to Consensus for a Hegselmann-Krause-Type Model with Distributed Time Delay

Alessandro Paolucci
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, UniversitÓ di L'Aquila, 67010 L'Aquila, Italy
alessandro.paolucci2@graduate.univaq.it



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.

Keywords: Hegselmann-Krause model, opinion formation, delay, consensus.

MSC: 34D05, 91D10, 34K20.

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