{
  "annotation_id": "7e837b94-f556-4c30-bdfb-549524c23c82",
  "date_created": "2026-03-02T18:01:35.850000Z",
  "date_modified": "2026-03-02T18:01:35.850000Z",
  "file_hash": "711d627240909f3b6e4a643aea677eaa6e2644630e21ee08f46b262ae480c9c3",
  "private": false,
  "record": {
    "abstract": "In this paper the existence and unicity of a stable periodic orbit is proven,\nfor a class of piecewise affine differential equations in dimension 3 or more,\nprovided their interaction structure is a negative feedback loop. It is also\nshown that the same systems converge toward a unique stable equilibrium point\nin dimension 2. This extends a theorem of Snoussi, which showed the existence\nof these orbits only. The considered class of equations is usually studied as a\nmodel of gene regulatory networks. It is not assumed that all decay rates are\nidentical, which is biologically irrelevant, but has been done in the vast\nmajority of previous studies. Our work relies on classical results about fixed\npoints of monotone, concave operators acting on positive variables. Moreover,\nthe used techniques are very likely to apply in more general contexts, opening\ndirections for future work.",
    "arxiv_id": "q-bio/0611028",
    "authors": [
      "Etienne Farcot",
      "Jean-Luc Gouz\u00e9"
    ],
    "categories": [
      "q-bio.QM",
      "math.DS"
    ],
    "title": "Periodic solutions of piecewise affine gene network models: the case of   a negative feedback loop",
    "url": "https://arxiv.org/abs/q-bio/0611028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eaa00f56-719c-4da6-a8dc-c25822ee9679",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}