{
  "abstract": "Traveling waves of activity in neural tissue can be halted by spatial inhomogeneity in synaptic coupling. We study an integrate-and-fire network in which each neuron fires once and the coupling decays exponentially. For this model the leading-edge firing map reduces exactly to a scalar equation for the wave speed in space, with a slow unstable and a fast stable homogeneous speed, $c_1$ and $c_2$, and a periodic modulation of the coupling enters this equation pointwise. Positive periodic waves terminate in folds. For slowly varying modulation the fold amplitude approaches a plateau set by the trough of the modulation, where the local bottleneck speed is $\\sqrt{c_1 c_2}$; the approach to the plateau is set by the local geometry of the trough. For rapidly varying modulation the fold amplitude grows linearly with frequency, with a slope given by a full-amplitude average over the integrated modulation profile; a weak-ripple truncation of that average overestimates the slope about 2.5-fold at the default coupling. A perturbative recursion in the amplitude gives the speed profile explicitly. We distinguish loss of the periodic wave from failure of a particular launch, and the excitatory regime $ε\\le 1$ from its sign-changing extension. The results are checked against direct integration of the reduced equation and first-spike firing-map simulations of the network.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33006",
  "author_total": 6,
  "authors": [
    {
      "name": "Jie Nissel"
    },
    {
      "name": "Ricardo Erazo-Toscano"
    },
    {
      "name": "Rosahn Bhattarai"
    },
    {
      "name": "Marius Osan"
    },
    {
      "name": "Mandeep Chauhan"
    },
    {
      "name": "Remus Osan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4df7xyr6m54q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33006",
  "fulltext_url": null,
  "id": "b4df7xyr6m54q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33006",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "arxiv",
      "q-bio.NC"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7214712307",
  "pdf_url": "https://arxiv.org/pdf/2609.33006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4df7xyr6m54q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.33006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33006"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure",
  "title_text": "Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:21Z",
  "url": "https://research.draconitic.com/paper/b4df7xyr6m54q",
  "venue": "arXiv",
  "versions": []
}