A nonlinear model of opinion formation on the sphere

Marco Caponigro; Anna Chiara Lai; Benedetto Piccoli

doi:10.3934/dcds.2015.35.4241

Article Contents

2015, Volume 35, Issue 9: 4241-4268. Doi: 10.3934/dcds.2015.35.4241

This issue Previous Article Global propagation of singularities for time dependent Hamilton-Jacobi equations Next Article A semi-Lagrangian scheme for a degenerate second order mean field game system

A nonlinear model of opinion formation on the sphere

1.
Équipe M2N - EA 7340, Conservatoire National des Arts et Métiers, Paris
2.
Dipartimento di Matematica e Fisica, Università degli studi di Roma Tre, Rome
3.
Department of Mathematical Sciences & Center for Computational and Integrative Biology, Rutgers University, Camden, NJ

Received: May 31, 2014

Revised: September 30, 2014

Published: May 2017

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Abstract

In this paper we present a model for opinion dynamics on the $d$-dimensional sphere based on classical consensus algorithms. The choice of the model is motivated by the analysis of the comprehensive literature on the subject, both from the mathematical and the sociological point of views. The resulting dynamics is highly nonlinear and therefore presents a rich structure. Equilibria and asymptotic behavior are then analysed and sufficient condition for consensus are established. Finally we address global stabilization and controllability.

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Mathematics Subject Classification: Primary: 91D10, 34A34; Secondary: 34H05, 91B69.

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