{
  "id": "2310.19700",
  "version": "v2",
  "published": "2023-10-30T16:22:24.000Z",
  "updated": "2024-07-18T09:06:46.000Z",
  "title": "Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions",
  "authors": [
    "Emiliano Cristiani",
    "Nadia Loy",
    "Marta Menci",
    "Andrea Tosin"
  ],
  "comment": "32 pages, 7 figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "cs.NA",
    "math.MP",
    "math.NA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-18T09:06:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q20",
      "35Q70",
      "92D50"
    ],
    "keywords": [
      "kinetic description",
      "continuous leader-follower transitions",
      "macroscopic limit",
      "swarming dynamics",
      "system featuring emerging leaders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}