Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction
Abstract
In this paper, we analyze a Hegselmann-Krause opinion formation model and a Cucker-Smale flocking model with attractive-repulsive interaction. To be precise, we investigate the situation in which the individuals involved in an opinion formation or a flocking process attract each other in certain time intervals and repeal each other in other ones. Under quite general assumptions, we prove the convergence to consensus for the Hegselmann-Krause model and the exhibition of asymptotic flocking for the Cucker-Smale model in presence of positive-negative interaction. With some additional conditions, we are able to improve the convergence to consensus for the solutions of the Hegselmann-Krause model, namely we establish an exponential convergence to consensus result.
Cite
@article{arxiv.2311.13238,
title = {Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction},
author = {Elisa Continelli and Cristina Pignotti},
journal= {arXiv preprint arXiv:2311.13238},
year = {2025}
}