On the control of the Hegselmann-Krause model with leadership and time delay

TL;DR

This paper studies how leadership can steer opinion formation in Hegselmann-Krause models with time delays, showing control is possible under certain small delay conditions through analytical and numerical methods.

Contribution

It introduces control strategies for Hegselmann-Krause models with pointwise and distributed delays, demonstrating leader influence under small delay assumptions.

Findings

Leader can control opinion dynamics with small delays

Control effectiveness demonstrated through analytical proofs

Numerical tests support theoretical results

Abstract

We analyze Hegselmann-Krause opinion formation models with leadership in presence of time delay effects. In particular, we consider a model with pointwise time variable time delay and a model with a distributed delay. In both cases we show that, when the delays satisfy suitable smallness conditions, then the leader can control the system, leading the group to any prefixed state. Some numerical tests illustrate our analytical results.