Macroscopic descriptions of follower-leader systems

Sara Bernardi, Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter

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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.
Original languageEnglish
Pages (from-to)981-1002
Number of pages22
JournalKinetic and Related Models
Issue number6
Early online date18 Nov 2021
Publication statusPublished - Dec 2021


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