Opinion dynamics under common influencer assumption or leadership control

TL;DR

This paper investigates opinion formation models with common influencers or independent leaders, demonstrating conditions for consensus convergence through theoretical analysis and numerical validation.

Contribution

It introduces a framework for analyzing opinion dynamics with non-universal interactions and leadership influence, providing new convergence results.

Findings

Asymptotic convergence to consensus is proven under certain conditions.

Numerical tests support the theoretical convergence results.

Models with common influencers or independent leaders are effectively analyzed.

Abstract

We study Hegselmann-Krause type opinion formation models with non-universal interaction and time-delayed coupling. We assume the presence of a common influencer between two different agents. Moreover, we explore two cases in which such an assumption does not hold but leaders with independent opinion are present. By using careful estimates on the system's trajectories, we are able to prove asymptotic convergence to consensus estimates. Some numerical tests illustrate the theoretical results.