Convergence to Consensus for a Hegselmann-Krause-Type Model with Distributed Time Delay
Keywords:
Hegselmann-Krause model, opinion formation, delay, consensus.Abstract
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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