{
  "id": "2502.09475",
  "version": "v1",
  "published": "2025-02-13T16:39:07.000Z",
  "updated": "2025-02-13T16:39:07.000Z",
  "title": "Extinction and Metastability of Pheromone-Roads in Stochastic Models for Foraging Walks of Ants",
  "authors": [
    "Saori Morimoto",
    "Makoto Katori",
    "Hiraku Nishimori"
  ],
  "comment": "LaTeX 18 pages, 8 figures",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.AO",
    "q-bio.PE"
  ],
  "abstract": "Macroscopic changes of group behavior of eusocial insects are studied from the viewpoint of non-equilibrium phase transitions. Recent combined study of experiments and mathematical modeling by the group led by the third author suggests that a species of garden ant switches the individual foraging walk from pheromone-mediated to visual-cues-mediated depending on situation. If an initial pheromone-road between the nest and food sources is a detour, ants using visual cues can pioneer shorter paths. These shorter paths are reinforced by pheromone secreted by following ants, and then the detour ceases to exist. Once the old pheromone-road extincts, there will be almost no chance to reconstruct it. Hence the extinction of pheromone-road is expected to be regarded as a phase transition to an absorbing state. We propose a discrete-time model on a square lattice consisting of switching random walks interacting though time-dependent pheromone field. The numerical study shows that the critical phenomena of the present extinction transitions of pheromone-roads do not seem to belong to the directed percolation universality class associated with the usual absorbing-state transition. The new aspects are cased by the coexistence and competition with newly creating pheromone-roads. In a regime in the extinction phase, the annihilating road shows metastability and takes long time-period to be replaced by a new road.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-13T16:39:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "foraging walk",
      "stochastic models",
      "extinction",
      "metastability",
      "time-dependent pheromone field"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}