{
  "annotation_id": "7ee91b97-d975-47d9-b554-2a2eebddcd02",
  "date_created": "2026-03-02T18:01:11.094000Z",
  "date_modified": "2026-03-02T18:01:11.094000Z",
  "file_hash": "b70a4e62594c940c6a222d72d9b4c324a7503120e80a016ddd2901e4c3cf07aa",
  "private": false,
  "record": {
    "abstract": "We generalize a model of Haeussler and von der Malsburg which describes the\nself-organized generation of retinotopic projections between two\none-dimensional discrete cell arrays on the basis of cooperative and\ncompetitive interactions of the individual synaptic contacts. Our generalized\nmodel is independent of the special geometry of the cell arrays and describes\nthe temporal evolution of the connection weights between cells on different\nmanifolds. By linearizing the equations of evolution around the stationary\nuniform state we determine the critical global growth rate for synapses onto\nthe tectum where an instability arises. Within a nonlinear analysis we use then\nthe methods of synergetics to adiabatically eliminate the stable modes near the\ninstability. The resulting order parameter equations describe the emergence of\nretinotopic projections from initially undifferentiated mappings independent of\ndimension and geometry.",
    "arxiv_id": "physics/0607253",
    "authors": [
      "Martin Guessmann",
      "Axel Pelster",
      "Guenter Wunner"
    ],
    "categories": [
      "physics.bio-ph"
    ],
    "doi": "10.1002/andp.200610243",
    "journal_ref": "Ann. Phys. (Leipzig) 16, 379 (2007)",
    "title": "Synergetic Analysis of the Haeussler-von der Malsburg Equations for   Manifolds of Arbitrary Geometry",
    "url": "https://arxiv.org/abs/physics/0607253"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "76afb084-9d2f-425f-93a2-d87fe2c12d39",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}