{
  "annotation_id": "5b1df4d8-a685-4dbd-9006-9b116308ece3",
  "date_created": "2026-03-02T18:00:28.873000Z",
  "date_modified": "2026-03-02T18:00:28.873000Z",
  "file_hash": "a182e4e70c43e1e2129f8f358c3872c39c5154a89b69f3a224f885c86a663a87",
  "private": false,
  "record": {
    "abstract": "We study the interfaces\u0027 time evolution in one-dimensional bistable extended\ndynamical systems with discrete time. The dynamics is governed by the\ncompetition between a local piece-wise affine bistable mapping and any\ncouplings given by the convolution with a function of bounded variation. We\nprove the existence of travelling wave interfaces, namely fronts, and the\nuniqueness of the corresponding selected velocity and shape. This selected\nvelocity is shown to be the propagating velocity for any interface, to depend\ncontinuously on the couplings and to increase with the symmetry parameter of\nthe local nonlinearity. We apply the results to several examples including\ndiscrete and continuous couplings, and the planar fronts\u0027 dynamics in\nmulti-dimensional Coupled Map Lattices. We eventually emphasize on the\nextension to other kinds of fronts and to a more general class of bistable\nextended mappings for which the couplings are allowed to be nonlinear and the\nlocal map to be smooth.",
    "arxiv_id": "patt-sol/9805006",
    "authors": [
      "R. Coutinho",
      "B. Fernandez"
    ],
    "categories": [
      "patt-sol",
      "math.DS",
      "nlin.PS"
    ],
    "doi": "10.1088/0951-7715/11/5/014",
    "title": "Fronts and interfaces in bistable extended mappings",
    "url": "https://arxiv.org/abs/patt-sol/9805006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cf69631-27e3-490a-a24d-7473a62d3e8b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}