{
  "abstract": "This paper presents a comprehensive machine learning framework for the analysis of a stage-structured predator–prey system incorporating the fear effect, intra-specific competition among juvenile predators, and maturation delay. The three-species model, comprising prey (N), juvenile predators (P1), and mature predators (P2), is governed by a non-linear ordinary differential equation system in which the prey growth rate is modulated by a fear factor 1/(1+kP2). We first establish the existence and local stability of the coexistence equilibrium E* = (16.02, 16.09, 32.19) and rigorously identify a supercritical Hopf bifurcation at a critical fear intensity kcrit ≈ 0.067, beyond which the equilibrium becomes unstable and a stable limit cycle emerges. Five machine learning methods are deployed and benchmarked: (i) Sparse Identification of Non-linear Dynamics (SINDy) with a generic polynomial library, which recovers the predator equations exactly (R2 = 1.0) and approximates the prey equation (R2 = 0.9997); (ii) Dynamic Mode Decomposition (DMD), whose linear assumption yields poor reconstruction (R2 = −2.885 for P2), demonstrating the inadequacy of linear methods for this non-linear system; (iii) Gaussian Process Regression (GPR) with a periodic–RBF composite kernel, achieving RMSE values of 1.92, 1.03, and 0.84 from sparse noisy observations; (iv) a physics-constrained function approximation for recovering population trajectories from incomplete data; and (v) a polynomial surrogate ODE model for derivative field approximation. Additionally, the effect of maturation delay τ on system stability is examined through delay differential equation analysis with a fourth-order Runge–Kutta integrator, revealing delay-induced destabilization and transitions to limit cycle dynamics at τ ≥ 10. All numerical results are independently verified and all performance metrics are computed from actual analyses. The framework provides a rigorous, reproducible methodology for applying modern data-driven methods to stage-structured ecological models.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Vellore Institute of Technology , , ,"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "G. Ramraj"
    },
    {
      "affs": [
        0
      ],
      "name": "T. Poornima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56k0ht6whzzfv.bib",
  "cited_by": 0,
  "doi": "10.3389/frai.2026.1887024",
  "fulltext_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13719457/?tool=EBI",
  "id": "56k0ht6whzzfv",
  "issns": [
    "2624-8212"
  ],
  "landing_url": "https://europepmc.org/article/PMC/PMC13719457",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Original Research"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
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  "openalex": "W7222527138",
  "pdf_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13719457/pdf/?tool=EBI",
  "pmcid": "PMC13719457",
  "pmid": "42964220",
  "published": "2026-10-16",
  "publisher": "Frontiers Media SA",
  "ris": "https://research.draconitic.com/paper/56k0ht6whzzfv.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:21:36Z",
      "native_id": "PMC:PMC13719457",
      "source": "europepmc",
      "url": "https://europepmc.org/article/PMC/PMC13719457"
    },
    {
      "first_seen": "2026-11-02T12:23:25Z",
      "native_id": "PMC13719457",
      "source": "pmc",
      "url": "https://doi.org/10.3389/frai.2026.1887024"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "openalex:2739|Mathematical and Theoretical Epidemiology and Ecology Models",
      "subfield": "epidemiology-public-health"
    }
  ],
  "title": "A machine learning framework for stage-structured predator–prey systems with fear effect: Sparse Identification, Gaussian Process Regression, and bifurcation analysis",
  "title_text": "A machine learning framework for stage-structured predator–prey systems with fear effect: Sparse Identification, Gaussian Process Regression, and bifurcation analysis",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T12:20:31Z",
  "url": "https://research.draconitic.com/paper/56k0ht6whzzfv",
  "venue": "Frontiers in artificial intelligence",
  "versions": []
}