A nonlinear model of opinion formation on the sphere

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.