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arXiv · 2508.08157

Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits

Young-Pil Choi·Chiara Cicolani·Cristina Pignotti
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Abstract

We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the same time, non-leaders update their opinions via interactions with their peers and the leaders, with time delays accounting for communication and decision-making lags. We prove the exponential convergence to consensus of the particle system, without imposing smallness assumptions on the delay parameters. Furthermore, we analyze the mean-field limit in two regimes: (i) with a fixed number of leaders and an infinite number of non-leaders, and (ii) with both populations tending to infinity, obtaining existence, uniqueness, and exponential decay estimates for the corresponding macroscopic models.

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Young-Pil Choi, Chiara Cicolani, Cristina Pignotti. 2025-08-11. Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits. https://doi.org/10.4310/cms.260326190826

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