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Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics

  • Nicola Vassena
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Abstract

This paper establishes that the system of ordinary differential equations arising from the sequential and distributive dual futile cycle has the structural capacity for Hopf bifurcations, whenever it is endowed with general parameter-rich kinetics, but it loses such capacity if it is endowed with mass action kinetics. The proof of the latter fact relies on a Routh-Hurwitz approach, improved by few preliminary structural considerations, but a decisive contribution came from ChatGPT Sol 5.6, which provided a nontrivial positivity certificate. A second purpose of the paper is indeed to document such AI-contribution, exploiting this well-studied toy-model, and to offer an example of the utilizability of such tools in the context of computer algebra and positivity certificates for large polynomials.

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Cite

BibTeXRIS
BibTeX
@misc{vassena2026sequential,
  title = {{Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics}},
  author = {Nicola Vassena},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.27081},
  eprint = {2608.27081},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27081},
}
RIS
TY  - UNPB
TI  - Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics
AU  - Nicola Vassena
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.27081
UR  - https://arxiv.org/abs/2608.27081
AB  - This paper establishes that the system of ordinary differential equations arising from the sequential and distributive dual futile cycle has the structural capacity for Hopf bifurcations, whenever it is endowed with general parameter-rich kinetics, but it loses such capacity if it is endowed with mass action kinetics. The proof of the latter fact relies on a Routh-Hurwitz approach, improved by few preliminary structural considerations, but a decisive contribution came from ChatGPT Sol 5.6, which provided a nontrivial positivity certificate. A second purpose of the paper is indeed to document such AI-contribution, exploiting this well-studied toy-model, and to offer an example of the utilizability of such tools in the context of computer algebra and positivity certificates for large polynomials.
ER  -