Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits
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| Format: | Preprint |
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2025
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| author | Choi, Young-Pil Cicolani, Chiara Pignotti, Cristina |
| author_facet | Choi, Young-Pil Cicolani, Chiara Pignotti, Cristina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_08157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits Choi, Young-Pil Cicolani, Chiara Pignotti, Cristina Analysis of PDEs Optimization and Control 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. |
| title | Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2508.08157 |