Macroscopic descriptions of follower-leader systems - Sorbonne Université
Journal Articles Kinetic and Related Models Year : 2021

Macroscopic descriptions of follower-leader systems

Abstract

The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities remains a challenge from the perspective of both modelling and analysis. In this paper we clarify relevant continuous macroscopic model equations that describe follower-leader interactions for a swarm where these two populations are fixed. We study the behaviour of the swarm over long and short time scales to shed light on the number of leaders needed to initiate swarm movement, according to the homogeneous or inhomogeneous nature of the interaction (alignment) kernel. The results indicate the crucial role played by the interaction kernel to model transient behaviour.
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Dates and versions

hal-03460617 , version 1 (01-12-2021)

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Sara Bernardi, Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J Painter. Macroscopic descriptions of follower-leader systems. Kinetic and Related Models , 2021, ⟨10.3934/krm.2021035⟩. ⟨hal-03460617⟩
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