{
  "annotation_id": "dc101871-16b9-4fb6-858c-a3a6f20d3c78",
  "date_created": "2026-03-02T18:00:29.441000Z",
  "date_modified": "2026-03-02T18:00:29.441000Z",
  "file_hash": "272a5205c0a5169ce35f920b19781583729ca369264e532a710cbd50806501fe",
  "private": false,
  "record": {
    "abstract": "Dispersion curves to a oscillatory reaction-diffusion system with the\nself-consistent flow have obtained by means of numerical calculations. The flow\nmodulates the shape of dispersion curves and characteristics of traveling\nwaves. The point of inflection which separates the dispersion curves into two\nbranches corresponding to trigger and phase waves, moves according to the value\nof the advection constant. The dynamics of phase wave in\nreaction-diffusion-advection equations has been studied by limit cycle\nperturbations. The dispersion relation obtained from the phase equation shows\nthat the competition between diffusion and advection constants modulates the\noscillation frequency from the bulk oscillation in the long-wave dynamics. Such\na competition implies that phase waves with the flow have a wider variety of\ndynamics than waves without the flow.",
    "arxiv_id": "patt-sol/9906010",
    "authors": [
      "Hiroyasu Yamada",
      "Toshiyuki Nakagaki"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "title": "Dispersion relations to oscillatory reaction-diffusion systems with the   self-consistent flow",
    "url": "https://arxiv.org/abs/patt-sol/9906010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2f693309-91dc-4848-b31e-49e6c2262d6b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}