IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v228y2025icp362-385.html
   My bibliography  Save this article

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

Author

Listed:
  • Cristiani, Emiliano
  • Loy, Nadia
  • Menci, Marta
  • Tosin, Andrea

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.

Suggested Citation

  • Cristiani, Emiliano & Loy, Nadia & Menci, Marta & Tosin, Andrea, 2025. "Kinetic description and macroscopic limit of swarming dynamics with continuous leader–follower transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 362-385.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:362-385
    DOI: 10.1016/j.matcom.2024.09.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424003616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.09.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:362-385. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.