Convergence to consensus results for Hegselmann-Krause type models with attractive-lacking interaction

Elisa Continelli; Cristina Pignotti

doi:10.3934/mcrf.2024029

Article Contents

2024, Volume 14, Issue 4: 1408-1427. Doi: 10.3934/mcrf.2024029

This issue Previous Article Lyapunov stability for measure differential equations Next Article Discontinuous solutions to the hamilton jacobi equation under second order interiority hypotheses

Convergence to consensus results for Hegselmann-Krause type models with attractive-lacking interaction

Elisa Continelli and
Cristina Pignotti^,

Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli Studi dell'Aquila, Via Vetoio, 67100 L'Aquila, Italy

^*Corresponding author: Cristina Pignotti
^*Corresponding author: Cristina Pignotti

Received: October 2023

Revised: March 2024

Early access: July 2024

Published online: July 2024

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Abstract

In this paper, we analyze a Hegselmann-Krause opinion formation model with attractive-lacking interaction. More precisely, we investigate the situation in which the agents involved in an opinion formation process interact among themselves but can eventually suspend the exchange of information among each other at some times. Under quite general assumptions, we prove the exponential convergence to consensus for the model in presence of possible lack of interaction. We are also able to extend the consensus estimate in the case of Hegselmann-Krause models with time delay effects.

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Mathematics Subject Classification: Primary: 34D05, 34K20; Secondary: 91D10.

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