Opinion Dynamics on Discourse Sheaves
@article{Hansen2021OpinionDO,
title={Opinion Dynamics on Discourse Sheaves},
author={Jakob Hansen and Robert Ghrist},
journal={SIAM J. Appl. Math.},
year={2021},
volume={81},
pages={2033-2060}
}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…
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References
SHOWING 1-10 OF 49 REFERENCES
A tutorial on modeling and analysis of dynamic social networks. Part I
- Computer ScienceAnnu. Rev. Control.
- 2017
Predictable Dynamics of Opinion Forming for Networks With Antagonistic Interactions
- MathematicsIEEE Transactions on Automatic Control
- 2015
A significant class of signed graphs is identified for which the linear dynamics are however predictable and many analogies with positive dynamical systems are shown, including those of adjacency matrices that are eventually positive.
Opinion Dynamics and the Evolution of Social Power in Influence Networks
- EconomicsSIAM Rev.
- 2015
This paper provides a rigorous mathematical formulation of the influence network dynamics, characterize its equilibria, and establish its convergence properties for all possible structures of the relative interpersonal weights and corresponding eigenvector centrality scores.
Dynamics of Opinion Forming in Structurally Balanced Social Networks
- Mathematics2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012
The paper shows that monotone dynamical systems, due to their order-preserving solutions, are natural candidates to describe the highly predictable process of opinion forming on structurally balanced networks.
Opinion dynamics in social networks with stubborn agents: An issue-based perspective
- Computer ScienceAutom.
- 2018
A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part II
- Computer ScienceAnnu. Rev. Control.
- 2018
Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications
- Mathematics, EconomicsSIAM J. Control. Optim.
- 2010
It is established that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents.