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arXiv · 2412.02620

The Dimension of the Disguised Toric Locus of a Reaction Network

Gheorghe Craciun·Abhishek Deshpande·Jiaxin Jin
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Abstract

Under mass-action kinetics, complex-balanced systems emerge from biochemical reaction networks and exhibit stable and predictable dynamics. For a reaction network $G$, the associated dynamical system is called $\textit{disguised toric}$ if it can yield a complex-balanced realization on a possibly different network $G_1$. This concept extends the robust properties of toric systems to those that are not inherently toric. In this work, we study the $\textit{disguised toric locus}$ of a reaction network - i.e., the set of positive rate constants that make the corresponding mass-action system disguised toric. Our primary focus is to compute the exact dimension of this locus. We subsequently apply our results to Thomas-type and circadian clock models.

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Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin. 2024-12-03. The Dimension of the Disguised Toric Locus of a Reaction Network. https://arxiv.org/abs/2412.02620

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