Dynamics of majority rule on hypergraphs

Author: 

Noonan, J
Lambiotte, R

Publication Date: 

25 August 2021

Journal: 

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

Last Updated: 

2021-10-12T06:51:30.977+01:00

Issue: 

2

Volume: 

104

DOI: 

10.1103/PhysRevE.104.024316

abstract: 

A broad range of dynamical systems involve multibody interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, namely the majority rule, and we investigate the possibility to represent and analyze the system by means of hypergraphs. We explore the formation of consensus, and we restrict our attention to interaction groups of size 3 in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or mean-field heterogeneity, and we recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

Symplectic id: 

1156866

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article