{
  "annotation_id": "a156135d-1293-4f40-b9a3-b24a439ba74d",
  "date_created": "2026-03-02T18:01:17.183000Z",
  "date_modified": "2026-03-02T18:01:17.183000Z",
  "file_hash": "39301553f7c77ccdc5a7310fec87d67bd685e874a06d92c5b1a74ccf6e4f974f",
  "private": false,
  "record": {
    "abstract": "The combination of complex networks and dynamic systems research is poised to\nyield some of the most interesting theoretic and applied scientific results\nalong the forthcoming decades. The present work addresses a particularly\nimportant related aspect, namely the quantification of how well separated can\nthe attractors be in dynamic systems underlined by four types of complex\nnetworks (Erd\\H{o}s-R\\\u0027enyi, Barab\\\u0027asi-Albert, Watts-Strogatz and as well as a\ngeographic model). Attention is focused on grandmother dynamic systems, where\neach state variable (associated to each node) is used to represent a specific\nprototype pattern (attractor). By assuming that the attractors spread their\ninfluence among its neighboring nodes through a diffusive process, it is\npossible to overlook the specific details of specific dynamics and focus\nattention on the separability among such attractors. This property is defined\nin terms of two separation indices (one individual to each prototype and the\nother considering also the immediate neighborhood) reflecting the balance and\nproximity to attractors revealed by the activation of the network after a\ndiffusive process. The separation index considering also the neighborhood was\nfound to be much more informative, while the best separability was observed for\nthe Watts-Strogatz and the geographic models. The effects of the involved\nparameters on the separability were investigated by correlation and path\nanalyses. The obtained results suggest the special importance of some\nmeasurements in underlying the relationship between topology and dynamics.",
    "arxiv_id": "physics/0701089",
    "authors": [
      "Luciano da Fontoura Costa"
    ],
    "categories": [
      "physics.data-an",
      "cond-mat.dis-nn",
      "physics.comp-ph"
    ],
    "title": "On the Separability of Attractors in Grandmother Dynamic Systems with   Structured Connectivity",
    "url": "https://arxiv.org/abs/physics/0701089"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cb6f9096-1d66-46b9-b8af-96a0caa7ed61",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}