Disguised toric dynamical systems
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Disguised toric dynamical systems. / Brustenga i Moncusí, Laura; Craciun, Gheorghe; Sorea, Miruna Ştefana.
In: Journal of Pure and Applied Algebra, Vol. 226, No. 8, 107035, 2022.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Disguised toric dynamical systems
AU - Brustenga i Moncusí, Laura
AU - Craciun, Gheorghe
AU - Sorea, Miruna Ştefana
N1 - Publisher Copyright: © 2022 Elsevier B.V.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
U2 - 10.1016/j.jpaa.2022.107035
DO - 10.1016/j.jpaa.2022.107035
M3 - Journal article
AN - SCOPUS:85124040357
VL - 226
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 8
M1 - 107035
ER -
ID: 342612037