Time-delayed opinion dynamics with leader-follower interactions: Consensus, stability, and mean-field limits
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.
Fields of Study & Subjects
Opinion Dynamics and Social Influence
Complex Network Analysis Techniques
Evolutionary Game Theory and Cooperation
Publication details
- Journal / source
- Communications in Mathematical Sciences
- Publisher
- International Press of Boston
- Volume
- 24
- Issue
- 4
- Pages
- 1073–1102
- Publication date
- 1 January 2026
- Language
- EN