On Lyapunov functions for open Hegselmann-Krause dynamics

Renato Vizuete; Paolo Frasca; Elena Panteley

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arXiv · 2303.07074

On Lyapunov functions for open Hegselmann-Krause dynamics

Renato Vizuete·Paolo Frasca·Elena Panteley

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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.

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Renato Vizuete, Paolo Frasca, Elena Panteley. 2023-03-13. On Lyapunov functions for open Hegselmann-Krause dynamics. https://arxiv.org/abs/2303.07074

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