Opinion Dynamics on Discourse Sheaves

2020/05/26 by Jakob Hansen, Robert Ghrist, Hansen, Jakob +1 · 18 citations
Mathematics · #55N30 (Secondary) #91D30 (Primary) #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AT #math.DS #msc:55N30 #msc:91D30

paper · pdf · doi:10.48550/arxiv.2005.12798

23 pages, 7 figures

arxiv created 2020/05/26 · arxiv updated 2020/05/27

Abstract

We introduce a novel class of Laplacians and diffusion dynamics on discourse sheaves as a model for network dynamics, with application to opinion dynamics on social networks. These sheaves are algebraic data structures tethered to a network (or more general space) that can represent various modes of communication, including selective opinion modulation and lying. After introducing the sheaf model, we develop a sheaf Laplacian in this context and show how to evolve both opinions and communications with diffusion dynamics over the network. Issues of controllability, reachability, bounded confidence, and harmonic extension are addressed using this framework.

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