Seminaire de Chiara Cicolani

– Title: 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.

– Bio:  Chiara Cicolani is a PhD student in Mathematics at the University of L’Aquila, Italy. She completed her studies at the University of L’Aquila with a Bachelor’s degree in Mathematics and a master’s degree in Mathematical modeling. Her research focuses on applied mathematics, with particular interests in control theory, multi-agent systems, and mathematical models in epidemiology and biology. She has collaborated with international research centers such as the Basque Center for Applied Mathematics (BCAM) in Spain and Yonsei University in Seoul, and has presented her work at various international conferences and workshops.

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