{
  "annotation_id": "ea086637-d7fa-4910-8e05-55fa6e9b3dc0",
  "date_created": "2026-03-02T18:01:00.899000Z",
  "date_modified": "2026-03-02T18:01:00.899000Z",
  "file_hash": "88c9c082ffdb3f66ecb42fdff896d55d43a9dafcd9c06b9d358ebe4ef6d96bf9",
  "private": false,
  "record": {
    "abstract": "Concepts from the Ergodic Theory are used to describe the existence of\nnon-transitive maps in attractors of phase synchronous chaotic systems. It is\nshown that for a class of phase-coherent systems, e.g. the sinusoidally forced\nChua\u0027s circuit and two coupled R{\\\"o}ssler oscillators, phase synchronization\nimplies that such maps exist. These ideas are also extended to other coupled\nchaotic systems. In addition, a phase for a chaotic attractor is defined from\nthe tangent vector of the flow. Finally, it is discussed how these maps can be\nused to real time detection of phase synchronization in experimental systems.",
    "arxiv_id": "physics/0507108",
    "authors": [
      "M. S. Baptista",
      "T. Pereira",
      "I. L. Caldas",
      "J. C. Sartorelli"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1016/j.physd.2005.10.003",
    "journal_ref": "Physica D 212, 216 (2005)",
    "title": "Non-transitive maps in phase synchronization",
    "url": "https://arxiv.org/abs/physics/0507108"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "615bdcef-e6c8-4691-b927-8ab0e5c22a79",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}