Kinetic description and macroscopic limit of swarming dynamics with continuous leader–follower transitions

Emiliano Cristiani, Nadia Loy, Marta Menci and Andrea Tosin

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 228, issue C, 362-385

Abstract: In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.

Keywords: Swarm dynamics; Transient leadership; Povzner–Boltzmann equation; Hydrodynamic limit; Non-conservative interactions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:228:y:2025:i:c:p:362-385

DOI: 10.1016/j.matcom.2024.09.006

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