The Dimension of the Disguised Toric Locus of a Reaction Network
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917855800328192 |
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| author | Craciun, Gheorghe Deshpande, Abhishek Jin, Jiaxin |
| author_facet | Craciun, Gheorghe Deshpande, Abhishek Jin, Jiaxin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Dimension of the Disguised Toric Locus of a Reaction Network Craciun, Gheorghe Deshpande, Abhishek Jin, Jiaxin Molecular Networks Dynamical Systems 14P05, 14P10, 14Q30, 34D23, 34C08, 37E99, 92C42 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. |
| title | The Dimension of the Disguised Toric Locus of a Reaction Network |
| topic | Molecular Networks Dynamical Systems 14P05, 14P10, 14Q30, 34D23, 34C08, 37E99, 92C42 |
| url | https://arxiv.org/abs/2412.02620 |