On Lyapunov functions for open Hegselmann-Krause dynamics
Systems and Control
2023-03-14 v1 Social and Information Networks
Systems and Control
Optimization and Control
Abstract
In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and departures are determined by homogeneous Poisson processes. Then, we provide a survey of Lyapunov functions based on global and local disagreement, whose asymptotic behavior can be used to measure the impact of arrivals and departures. After proving analytical results on these Lyapunov functions in the open system, we illustrate them through numerical simulations in two scenarios characterized by a different number of expected agents.
Cite
@article{arxiv.2303.07074,
title = {On Lyapunov functions for open Hegselmann-Krause dynamics},
author = {Renato Vizuete and Paolo Frasca and Elena Panteley},
journal= {arXiv preprint arXiv:2303.07074},
year = {2023}
}
Comments
17 pages, 2 figures