Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

A nonlinear model of opinion formation on the sphere

Pages: 4241 - 4268, Volume 35, Issue 9, September 2015      doi:10.3934/dcds.2015.35.4241

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Marco Caponigro - Équipe M2N - EA 7340, Conservatoire National des Arts et Métiers, Paris, France (email)
Anna Chiara Lai - Dipartimento di Matematica e Fisica, Università degli studi di Roma Tre, Rome, Italy (email)
Benedetto Piccoli - Department of Mathematical Sciences & Center for Computational and Integrative Biology, Rutgers University, Camden, NJ, United States (email)

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.

Keywords:  Opinion formation, multiagent dynamics, nonlinear dynamical systems, modeling, control.
Mathematics Subject Classification:  Primary: 91D10, 34A34; Secondary: 34H05, 91B69.

Received: June 2014;      Revised: October 2014;      Available Online: April 2015.