Asymptotic analysis of a Cucker-Smale system with leadership and distributed delay

TL;DR

This paper extends the analysis of a Cucker-Smale flocking model with hierarchical leadership and distributed delay, proving convergence to consensus and flocking behavior under various conditions, including a changing leader velocity.

Contribution

It introduces new convergence and flocking results for a generalized Cucker-Smale model with hierarchical leadership, distributed delay, and a dynamic leader velocity.

Findings

Proves convergence to consensus for models with distributed delay.

Establishes flocking estimates for general interaction potentials.

Shows flocking behavior when the leader's velocity can change under certain conditions.

Abstract

We extend the analysis developed in [33] in order to prove convergence to consensus results for a Cucker-Smale type model with hierarchical leadership and distributed delay. Flocking estimates are obtained for a general interaction potential with divergent tail. We analyze also the model when the ultimate leader can change its velocity. In this case we give a flocking result under suitable conditions on the leader's acceleration.