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  "slug": "reverse-reaction-attracting-oscillations",
  "title": "A reverse reaction can create attracting oscillations",
  "shortTitle": "One reverse arrow changes the dynamics",
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  "oneLine": "An explicit three-species mass-action network gains an attracting periodic orbit when one reverse reaction is restored, while the deleted network converges globally.",
  "abstract": "This unrefereed candidate gives explicit three-species mass-action counterexamples to three general isolated-intermediate reduction conjectures of Feliu and Kaihnsa. An integer-rate trimolecular network has a nondegenerate supercritical Hopf bifurcation, whereas deleting one reverse reaction leaves a system that converges globally to its unique positive equilibrium for every positive choice of the remaining rates. An exact one-parameter family classifies the first Lyapunov coefficient except at one explicitly isolated degenerate value. The result does not challenge the source paper's restricted theorem and does not resolve its motivating dual-phosphorylation question.",
  "datePublished": "2026-10-18",
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    "name": "General isolated-intermediate reduction conjectures",
    "url": "https://doi.org/10.1111/sapm.70268"
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    "A three-species six-reaction trimolecular mass-action network has a nondegenerate supercritical Hopf bifurcation after one reverse reaction is added.",
    "Deleting that reverse reaction yields global convergence to the unique positive equilibrium for every positive retained rate choice.",
    "An exact one-parameter family gives a closed Hopf locus and a first-Lyapunov-coefficient polynomial with one isolated positive degeneracy.",
    "The construction refutes the three general conjectures but leaves the source paper's restricted theorem and motivating dual-phosphorylation problem intact."
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    {
      "citation": "Feliu and Kaihnsa (2026), Network reduction and absence of Hopf bifurcations in dual phosphorylation networks with three intermediates: source theorem and conjectures.",
      "url": "https://doi.org/10.1111/sapm.70268",
      "doi": "10.1111/sapm.70268"
    },
    {
      "citation": "Banaji (2020), Building oscillatory chemical reaction networks by adding reversible reactions: close methodological antecedent.",
      "url": "https://doi.org/10.1137/19M1270975",
      "doi": "10.1137/19M1270975"
    },
    {
      "citation": "Banaji, Boros and Hofbauer (2025), The inheritance of local bifurcations in mass action networks: nearby bifurcation-inheritance theory.",
      "url": "https://doi.org/10.1007/s00332-025-10165-4",
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