Stability analysis of a socially inspired adaptive voter model

Emmanuel Kravitzch (1) , Yezekael Hayel (1) , Vineeth Varma (2) , Antoine Berthet (3)

1 LIA - Laboratoire Informatique d'Avignon
2 CRAN - Centre de Recherche en Automatique de Nancy
3 L2S - Laboratoire des signaux et systèmes

In this letter, we study an instance of continuous-time voter model over directed graphs on social networks with a specific refinement: the agents can break or create new links in the graph. The edges of the graph thus co-evolve with the agents’ spin. Specifically, the agents may break their links with neighbours of different spin, and create links their 2-hop neighbours, provided they have same spin. We characterize the absorbing configurations and present a particular case that corresponds to a single agent facing two antagonistic ideologies. By asymptotic analysis, we observe two regimes depending on the parameters: in one regime, hesitation disappears rapidly, while when the link creation rate is high enough, slow extinction occurs. We compute the threshold value and illustrate these results with numerical simulations.

Mots clés: Adaptive networks; stochastic models

Domaines: Probabilités [math.PR]; Système multi-agents [cs.MA]; Modélisation et simulation; Réseaux sociaux et d'information [cs.SI]

Emmanuel Kravitzch, Yezekael Hayel, Vineeth Varma, Antoine Berthet. Stability analysis of a socially inspired adaptive voter model. IEEE Control Systems Letters, 2023, 7, pp.175-180. ⟨10.1109/LCSYS.2022.3185386⟩. ⟨hal-03608386⟩