{
  "abstract": "We establish a phase reduction and a converse realization theorem for front dynamics in one-dimensional periodic reaction-diffusion-advection equations. For sufficiently large periods under local bistability, and sufficiently small periods when the homogenized equation admits a stationary front, we construct strictly ordered invariant front families that are normally exponentially attracting and locally complete for entire orbits. Modulo spatial-period translations, the dynamics on each family reduces exactly to a circle flow: rotations correspond to propagating pulsating fronts, equilibria to stationary fronts, and connecting orbits to transition fronts between stationary fronts. Conversely, every smooth circle flow can be realized, up to time-preserving topological conjugacy, as the quotient dynamics of such a family for a periodic, locally bistable equation with constant diffusion and no advection. Realizations with a Cantor set of stationary phases and a connecting orbit in each complementary interval illustrate the richness of front dynamics in these media. We also obtain first-order phase-velocity expansions in both period limits, quantitative propagation laws near zero frozen speed, and global exponential orbital stability of propagating pulsating fronts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34228",
  "author_total": 3,
  "authors": [
    {
      "name": "Weiwei Ding"
    },
    {
      "name": "Xing Liang"
    },
    {
      "name": "Linfeng Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zgwxneac230x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34228",
  "fulltext_url": null,
  "id": "9zgwxneac230x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34228",
  "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",
      "math.DS"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7223895426",
  "pdf_url": "https://arxiv.org/pdf/2610.34228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zgwxneac230x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Bistable fronts in periodic media: phase reduction and realization of circle flows",
  "title_text": "Bistable fronts in periodic media: phase reduction and realization of circle flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9zgwxneac230x",
  "venue": "arXiv",
  "versions": []
}