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PreprintCC BY 4.0arXiv

Bulk stability of bimolecular stochastic chemical reaction networks

  • Andrea Agazzi
  • Lucie Laurence
Open at sourcePDFDOICite

Abstract

We establish criteria for stability in the bulk of planar stochastic chemical reaction networks with mass-action kinetics. Using Poincaré compactification, we characterize the asymptotic drift and show how stochastic fluctuations can prevent escape along transversally repulsive branches of the limiting deterministic flow. We construct a Lyapunov function by combining local estimates near these branches with dissipative estimates in the neighboring regions. The criteria cover a wide class of networks and in particular apply beyond weakly reversible and strongly endotactic networks. Together with compatible boundary estimates, these criteria imply positive recurrence.

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Cite

BibTeXRIS
BibTeX
@misc{agazzi2026bulk,
  title = {{Bulk stability of bimolecular stochastic chemical reaction networks}},
  author = {Andrea Agazzi and Lucie Laurence},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31550},
  eprint = {2610.31550},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31550},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bulk stability of bimolecular stochastic chemical reaction networks
AU  - Andrea Agazzi
AU  - Lucie Laurence
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31550
UR  - https://arxiv.org/abs/2610.31550
AB  - We establish criteria for stability in the bulk of planar stochastic chemical reaction networks with mass-action kinetics. Using Poincaré compactification, we characterize the asymptotic drift and show how stochastic fluctuations can prevent escape along transversally repulsive branches of the limiting deterministic flow. We construct a Lyapunov function by combining local estimates near these branches with dissipative estimates in the neighboring regions. The criteria cover a wide class of networks and in particular apply beyond weakly reversible and strongly endotactic networks. Together with compatible boundary estimates, these criteria imply positive recurrence.
ER  -