{
  "abstract": "Repeated decisions exhibit temporal structures such as persistence, direction-dependent switching, recurrent alternation, and abrupt transitions. We examine the generative sufficiency of a two-dimensional fast-slow dynamical system. The system combines a cubic fast equation with linear slow feedback and is analyzed through its equilibrium geometry, trace-determinant structure, equilibrium-fold loci, candidate Hopf boundaries, and singular critical manifold. An explicit observation operator projects continuous trajectories to a scalar signal and applies a binary readout, separating latent state-space dynamics from observable behavior. The analysis establishes a unique-equilibrium regime and, for suitable parameters, a three-equilibrium wedge with a central saddle. The outer equilibria are attracting only where their traces are negative. The analysis also identifies the simple-zero condition required for ordinary saddle-nodes, trace-zero positive-determinant spectral boundaries compatible with oscillatory instability, and the attracting and repelling branches of the critical manifold. Prescribed nonautonomous sweeps numerically illustrate direction-dependent switching (T1), transient episodic recurrent switching (T2), and an abrupt localized regime shift (T3). The attracting-equilibrium regime associated with prolonged state retention (T4) is characterized analytically. The resulting correspondence is intended as a test of generative sufficiency at the level of observable temporal organization, rather than as an identification or empirical validation of latent cognitive mechanisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15918",
  "author_total": 2,
  "authors": [
    {
      "name": "Furkan Emre Isik"
    },
    {
      "name": "Ali Demirci"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nq9y72vj66xw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15918",
  "fulltext_url": null,
  "id": "4nq9y72vj66xw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15918",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "arxiv",
      "q-bio.NC"
    ],
    [
      "openalex",
      "2805|Neural dynamics and brain function"
    ]
  ],
  "openalex": "W7213351878",
  "pdf_url": "https://arxiv.org/pdf/2609.15918",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nq9y72vj66xw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15918",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15918"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Decision-Related Cognitive Signatures from Fast-Slow Dynamics: A Low-Dimensional Observation-Operator Framework",
  "title_text": "Decision-Related Cognitive Signatures from Fast-Slow Dynamics: A Low-Dimensional Observation-Operator Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:30Z",
  "url": "https://research.draconitic.com/paper/4nq9y72vj66xw",
  "venue": "arXiv",
  "versions": []
}