Asymptotic analysis of continuous opinion dynamics models under bounded confidence

Domenica Borra; Tommaso Lorenzi

doi:10.3934/cpaa.2013.12.1487

Article Contents

2013, Volume 12, Issue 3: 1487-1499. Doi: 10.3934/cpaa.2013.12.1487

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Asymptotic analysis of continuous opinion dynamics models under bounded confidence

Domenica Borra^1, and
Tommaso Lorenzi^1,

1.
Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino

Received: April 30, 2012

Revised: June 30, 2012

Published: April 2013

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Abstract

This paper deals with the asymptotic behavior of mathematical models for opinion dynamics under bounded confidence of Deffuant-Weisbuch type. Focusing on the Cauchy Problem related to compromise models with homogeneous bound of confidence, a general well-posedness result is provided and a systematic study of the asymptotic behavior in time of the solution is developed. More in detail, we prove a theorem that establishes the weak convergence of the solution to a sum of Dirac masses and characterizes the concentration points for different values of the model parameters. Analytical results are illustrated by means of numerical simulations.

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Mathematics Subject Classification: Primary: 35R09, 35B40; Secondary: 91D10.

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