# The Dimension of the Disguised Toric Locus of a Reaction Network

Source: [The Dimension of the Disguised Toric Locus of a Reaction Network](<https://www.sota2.com/research/paper/68fa5cae1e209131ce9d345f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:12.282Z

Authors: Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin

Published: 2024-12-03T17:46:53.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2412.02620>)

[PDF](<https://arxiv.org/pdf/2412.02620.pdf>)