Stochastic versus deterministic consensus dynamics on graphs
Dynamical Systems
2019-01-31 v1
Abstract
We study two agent based models of opinion formation - one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the models in all possible cases of graph topology. We are especially interested in the emergence of a consensus among the agents and provide a condition on the graph that is necessary and sufficient for convergence to a consensus in both models. This investigation reveals several contrasts between the models - notably the convergence rates - which are explored through analytical arguments and several numerical experiments.
Cite
@article{arxiv.1901.10756,
title = {Stochastic versus deterministic consensus dynamics on graphs},
author = {Dylan Weber and Ryan Theisen and Sebastien Motsch},
journal= {arXiv preprint arXiv:1901.10756},
year = {2019}
}