Disguised toric dynamical systems

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  • Laura Brustenga i Moncusí
  • Gheorghe Craciun
  • Miruna Ştefana Sorea

We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus on complex balanced mass-action systems, which have also been called toric. They are known or conjectured to enjoy very strong dynamical properties, such as existence and uniqueness of positive steady states, local and global stability, persistence, and permanence. We consider the class of disguised toric dynamical systems, which contains toric dynamical systems, and to which all dynamical properties mentioned above extend naturally. By means of (real) algebraic geometry we show that some reaction networks have an empty toric locus or a toric locus of Lebesgue measure zero in parameter space, while their disguised toric locus is of positive measure. We also propose some algorithms one can use to detect the disguised toric locus.

OriginalsprogEngelsk
Artikelnummer107035
TidsskriftJournal of Pure and Applied Algebra
Vol/bind226
Udgave nummer8
ISSN0022-4049
DOI
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
The authors would like to thank Bernd Sturmfels for bringing the team together, for giving us the opportunity to work on this project in the nice environment of the Nonlinear Algebra group at the Max Planck Institute for Mathematics in the Sciences, in Leipzig, and for his inspiring suggestions and comments. The authors would like to acknowledge the support of the Max Planck Institute for Mathematics in the Sciences, where most of this work was carried out. LBM's contribution has been supported by the Novo Nordisk Foundation grant NNF18OC0052483. GC was supported by NSF grants DMS-1816238 and DMS-2051568 and by a Simons Foundation fellowship. MSS thanks Antonio Lerario and Andrei Agrachev for their support and excellent working conditions during her postdoc at SISSA, Trieste.

Funding Information:
The authors would like to thank Bernd Sturmfels for bringing the team together, for giving us the opportunity to work on this project in the nice environment of the Nonlinear Algebra group at the Max Planck Institute for Mathematics in the Sciences, in Leipzig, and for his inspiring suggestions and comments. The authors would like to acknowledge the support of the Max Planck Institute for Mathematics in the Sciences, where most of this work was carried out. LBM's contribution has been supported by the Novo Nordisk Foundation grant NNF18OC0052483 . GC was supported by NSF grants DMS-1816238 and DMS-2051568 and by a Simons Foundation fellowship . MSS thanks Antonio Lerario and Andrei Agrachev for their support and excellent working conditions during her postdoc at SISSA, Trieste.

Publisher Copyright:
© 2022 Elsevier B.V.

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