Leader-Follower Dynamics

TL;DR

This paper extends the Leader-Follower opinion dynamics model to include social relationships, dynamic degrees, high-dimensional opinions, and multiple leader groups, providing theoretical insights into stability and consensus conditions.

Contribution

It introduces a generalized Leader-Follower model with new features and offers theoretical analysis of stability and consensus in complex social influence scenarios.

Findings

Conditions for asymptotic stability identified

Scenarios where few leaders dominate the population analyzed

Model extensions enable more realistic social influence representation

Abstract

The original Leader-Follower model, proposed in \cite{zhao2018understanding}, categorizes agents with opinions in $[-1,1]$ into a follower group, a leader group with a positive target opinion in $[0,1]$, and a leader group with a negative target opinion in $[-1,0]$. Leaders maintain a constant attraction to their target, blending it with the average opinion of their group neighbors at each update. Followers, on the other hand, have a constant attraction to the average opinion of their leader group's opinion neighbors, also integrating it with their group neighbors' average opinion. This model was numerically studied in \cite{zhao2018understanding}. This paper extends the Leader-Follower model to include a social relationship, variable degrees over time, high-dimensional opinions, and a flexible number of leader groups. We theoretically investigate conditions for asymptotic stability or consensus, particularly in scenarios where a few leaders can dominate the entire population.