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arXiv · 2311.13238

Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction

Elisa Continelli·Cristina Pignotti
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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.

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Elisa Continelli, Cristina Pignotti. 2023-11-22. Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction. https://doi.org/10.4310/cms.250607103236

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