{
  "abstract": "Hamiltonian and Lagrangian mechanics are powerful frameworks for analyzing physical systems. Previous work has extended these formalisms to ecological systems, such as the predator-prey Lotka-Volterra (LV) system. In this Article, we derive a canonical Lagrangian for the two-dimensional LV model directly from its Hamiltonian representation. We find that the two-dimensional LV system admits a standard canonical Lagrangian formulation with one degree of freedom and a non-quadratic kinetic structure. This formulation admits a mechanical interpretation in terms of a particle moving in a potential well, where the non-standard kinetic structure produces a position-dependent damping term that can instead act as \"revving.\" The derivation provides a direct connection between predator-prey dynamics and a canonical formulation of mechanical dynamics. As a verification of the construction, we apply Noether's procedure to the explicitly time-independent derived Lagrangian and reveal that the well-known Hamiltonian of the LV system is the corresponding conserved quantity. We also uncover a subtle redundancy associated with the choice of canonical momentum and its identification with the original population variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14747",
  "author_total": 2,
  "authors": [
    {
      "name": "Dima Watkins"
    },
    {
      "name": "Gene Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bvfx0gyv1xqe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14747",
  "fulltext_url": null,
  "id": "2bvfx0gyv1xqe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14747",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7213254754",
  "pdf_url": "https://arxiv.org/pdf/2609.14747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bvfx0gyv1xqe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Canonical Lagrangian Formulation of the Two-Dimensional Lotka-Volterra System",
  "title_text": "A Canonical Lagrangian Formulation of the Two-Dimensional Lotka-Volterra System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2bvfx0gyv1xqe",
  "venue": "arXiv",
  "versions": []
}