Deterministic Versus Stochastic Consensus Dynamics on Graphs

Dylan Weber, Ryan Theisen, Sebastien Motsch

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
JournalJournal of Statistical Physics
DOIs
StatePublished - Jan 1 2019

Fingerprint

Graph in graph theory
Agent-based Model
Long-time Behavior
topology
Numerical Experiment
Model
Sufficient
Topology
Necessary

Keywords

  • Agent based modeling
  • Consensus dynamics
  • Deterministic modeling
  • Dynamical systems
  • Network dynamics
  • Stochastic modeling

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Deterministic Versus Stochastic Consensus Dynamics on Graphs. / Weber, Dylan; Theisen, Ryan; Motsch, Sebastien.

In: Journal of Statistical Physics, 01.01.2019.

Research output: Contribution to journalArticle

@article{fe110ea203a54bf1b5ef215637960e71,
title = "Deterministic Versus Stochastic Consensus Dynamics on Graphs",
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.",
keywords = "Agent based modeling, Consensus dynamics, Deterministic modeling, Dynamical systems, Network dynamics, Stochastic modeling",
author = "Dylan Weber and Ryan Theisen and Sebastien Motsch",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10955-019-02293-5",
language = "English (US)",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",

}

TY - JOUR

T1 - Deterministic Versus Stochastic Consensus Dynamics on Graphs

AU - Weber, Dylan

AU - Theisen, Ryan

AU - Motsch, Sebastien

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Agent based modeling

KW - Consensus dynamics

KW - Deterministic modeling

KW - Dynamical systems

KW - Network dynamics

KW - Stochastic modeling

UR - http://www.scopus.com/inward/record.url?scp=85065015905&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065015905&partnerID=8YFLogxK

U2 - 10.1007/s10955-019-02293-5

DO - 10.1007/s10955-019-02293-5

M3 - Article

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -