Continuous-time Discontinuous Equations in Bounded Confidence Opinion Dynamics
Optimization and Control
2011-11-18 v4 Social and Information Networks
Systems and Control
Dynamical Systems
Abstract
This report studies a continuous-time version of the well-known Hegselmann-Krause model of opinion dynamics with bounded confidence. As the equations of this model have discontinuous right-hand side, we study their Krasovskii solutions. We present results about existence and completeness of solutions, and asymptotical convergence to equilibria featuring a "clusterization" of opinions. The robustness of such equilibria to small perturbations is also studied.
Keywords
Cite
@article{arxiv.1010.0066,
title = {Continuous-time Discontinuous Equations in Bounded Confidence Opinion Dynamics},
author = {Francesca Ceragioli and Paolo Frasca},
journal= {arXiv preprint arXiv:1010.0066},
year = {2011}
}
Comments
16 pages, no figures - v4: revised proof of Theorem 2