European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

Alternative equations for studying bifurcations in mass action networks

MS50-05

13 Jul 2026, 17:00

20m

11.02 - HS (University of Graz)

Minisymposium Talk Systems Biology and Biochemical Networks Dynamical Analysis of Biochemical Reaction Networks

Speaker

Murad Banaji (Lancaster University)

Description

I'll outline some recent results on the geometry of the positive equilibrium sets of mass action networks. We obtain useful parameterisations of equilibria and bounds on the number of (positive, nondegenerate) equilibria a mass action network can admit on any stoichiometric class. The techniques also lead to new approaches to studying bifurcations in mass action networks. Sometimes, via relatively simple calculations, we are able to guarantee or rule out particular bifurcations in a network or class of networks. Moreover, in some cases, the theory gives us tools to obtain explicit parameterisations of bifurcation sets.

Bibliography

@article{BF2025,
Title = {{Positive equilibria in mass action networks: geometry and bounds}},
Author = {Murad Banaji and Elisenda Feliu},
Archiveprefix = {arXiv},
Eprint = {2409.06877},
Year = {2025},
note = {\href{https://arxiv.org/pdf/2409.06877.pdf}{arXiv:2409.06877}}
}

@article{BBH2024,
      title = {Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity},
      volume = {112},
      issn = {0924-090X, 1573-269X},
      url = {https://link.springer.com/10.1007/s11071-024-10068-1},
      doi = {10.1007/s11071-024-10068-1},
      language = {en},
      number = {23},
      urldate = {2026-03-19},
      journal = {Nonlinear Dynamics},
      author = {Banaji, Murad and Boros, Balázs and Hofbauer, Josef},
      month = dec,
      year = {2024},
      pages = {21425--21448},
}