{
  "annotation_id": "f8886a86-01c5-4e63-b636-d977a3ca91c0",
  "date_created": "2026-02-17T05:53:08.609000Z",
  "date_modified": "2026-02-17T05:53:08.609000Z",
  "file_hash": "84e2bd4ac1078b369b134b0692ccd58d57d60bbd124c76d2db50d355c9e3bbbc",
  "private": false,
  "record": {
    "abstract": "This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system and provide a rigorous analysis of the conditions required for vegetation survival. Our results identify a critical patch size governed by the trade-off between local growth and boundary losses; habitats smaller than this threshold lead to inevitable extinction. Furthermore, we derive a critical maximal biomass density below which the population collapses to a desert state, regardless of the domain size. We determine stability criteria for stationary solutions and describe the emergence of stable, non-trivial biomass distributions. Numerical experiments comparing sub-Gaussian and super-Gaussian kernels confirm that non-local dispersal mechanisms, particularly those with fat tails, enhance ecosystem resilience by allowing vegetation to persist in smaller, fragmented habitats than predicted by classical local diffusion models.",
    "arxiv_id": "2601.06681",
    "authors": [
      "Maciej Tadej",
      "Ricardo Martinez-Garcia",
      "Michael Hecht"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes",
    "url": "https://arxiv.org/abs/2601.06681",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9a019e8e-9771-419d-b79a-840cd88e7189",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}