A nonlinear model of opinion formation on the sphere | Zendy

Marco Caponigro | Zendy; Anna Chiara Lai | Zendy; Benedetto Piccoli | Zendy

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A nonlinear model of opinion formation on the sphere

Author(s) -

Marco Caponigro,

Anna Chiara Lai,

Benedetto Piccoli

Publication year - 2015

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2015.35.4241

Subject(s) - controllability , nonlinear system , mathematical economics , subject (documents) , point (geometry) , dynamics (music) , mathematics , computer science , statistical physics , mathematical optimization , sociology , physics , geometry , pedagogy , quantum mechanics , library science

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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