{
  "annotation_id": "f9fc0482-9c22-470a-8d8f-df5578f2d9be",
  "date_created": "2026-03-02T18:00:28.850000Z",
  "date_modified": "2026-03-02T18:00:28.850000Z",
  "file_hash": "b37bb476190204bd33790a0f72fc0529ac17e894b71ea6a209a47fb9013f360b",
  "private": false,
  "record": {
    "abstract": "An asymptotic method for finding instabilities of arbitrary $d$-dimensional\nlarge-amplitude patterns in a wide class of reaction-diffusion systems is\npresented. The complete stability analysis of 2- and 3-dimensional localized\npatterns is carried out. It is shown that in the considered class of systems\nthe criteria for different types of instabilities are universal. The specific\nnonlinearities enter the criteria only via three numerical constants of order\none. The performed analysis explains the self-organization scenarios observed\nin the recent experiments and numerical simulations of some concrete\nreaction-diffusion systems.",
    "arxiv_id": "patt-sol/9603001",
    "authors": [
      "C. B. Muratov",
      "V. V. Osipov"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.53.3101",
    "journal_ref": "Phys. Rev. E 53, 3101 (1996).",
    "title": "General theory of instabilities for patterns with sharp interfaces in   reaction-diffusion systems",
    "url": "https://arxiv.org/abs/patt-sol/9603001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "085358f9-5bbb-47af-b56d-7fbb19dee7cf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}