{
  "annotation_id": "976c863c-5c3a-4dc6-88e3-1a5503d324c4",
  "date_created": "2026-03-02T18:00:28.862000Z",
  "date_modified": "2026-03-02T18:00:28.862000Z",
  "file_hash": "719e46ec877c186ec162b871fb63940bcc844313330fb7e1a981c968a931dea7",
  "private": false,
  "record": {
    "abstract": "Near a parity breaking front bifurcation, small perturbations may reverse the\npropagation direction of fronts. Often this results in nonsteady asymptotic\nmotion such as breathing and domain breakup. Exploiting the time scale\ndifferences of an activator-inhibitor model and the proximity to the front\nbifurcation, we derive equations of motion for planar and circular fronts. The\nequations involve a translational degree of freedom and an order parameter\ndescribing transitions between left and right propagating fronts.\nPerturbations, such as a space dependent advective field or uniform curvature\n(axisymmetric spots), couple these two degrees of freedom. In both cases this\nleads to a transition from stationary to oscillating fronts as the parity\nbreaking bifurcation is approached. For axisymmetric spots, two additional\ndynamic behaviors are found: rebound and collapse.",
    "arxiv_id": "patt-sol/9701010",
    "authors": [
      "Aric Hagberg",
      "Ehud Meron",
      "I. Rubinstein",
      "B. Zaltzman"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.55.4450",
    "journal_ref": "Physical Review E 55, 4450 (1997)",
    "title": "Order Parameter Equations for Front Transitions: Planar and Circular   Fronts",
    "url": "https://arxiv.org/abs/patt-sol/9701010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6e5278c0-cf21-45f9-b503-7a25d5d53c5f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}