A nonlinear model of opinion formation on the sphere

Marco Caponigro (1) , Anna Chiara Lai (2) , Benedetto Piccoli (3)

1 M2N - Modélisation mathématique et numérique
2 Dipartimento di Scienze di Base e Applicate per l'Ingegneria
3 Rutgers University, Department of Mathematics

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 behaviour are then analysed and sufficient condition for consensus are established.

Mots clés: multiagent dynamics; control; nonlinear dynamical systems; Opinion formation; modeling

Domaines: Optimisation et contrôle [math.OC]

Marco Caponigro, Anna Chiara Lai, Benedetto Piccoli. A nonlinear model of opinion formation on the sphere. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9), pp.4241-4268. ⟨10.3934/dcds.2015.35.4241⟩. ⟨hal-00995139v2⟩