Mixed Leader-Follower Dynamics

TL;DR

This paper extends the Leader-Follower model to include dynamic degrees, high-dimensional opinions, and multiple leader groups, analyzing conditions for consensus and leadership dominance in complex opinion dynamics.

Contribution

It introduces a generalized mixed leader-follower model with time-varying degrees, high-dimensional opinions, and multiple leaders, providing new insights into consensus formation and leadership influence.

Findings

Few leaders can dominate the entire population.

Consensus can be achieved under certain conditions.

Dynamic degrees and high-dimensional opinions influence the opinion dynamics.

Abstract

The original Leader-Follower (LF) model partitions all agents whose opinion is a number in $[-1,1]$ to a follower group, a leader group with a positive target opinion in $[0,1]$ and a leader group with a negative target opinion in $[-1,0]$. A leader group agent has a constant degree to its target and mixes it with the average opinion of its group neighbors at each update. A follower has a constant degree to the average opinion of the opinion neighbors of each leader group and mixes it with the average opinion of its group neighbors at each update. In this paper, we consider a variant of the LF model, namely the mixed model, in which the degrees can vary over time, the opinions can be high dimensional, and the number of leader groups can be more than two. We investigate circumstances under which all agents achieve a consensus. In particular, a few leaders can dominate the whole population.