Stability Analysis of a Socially Inspired Adaptive Voter Model

Abstract

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">co-evolve</i> 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.