Decomposable and essentially univariate mass-action systems: Extensions of the deficiency one theorem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913712795811840 |
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| author | Deshpande, Abhishek Müller, Stefan |
| author_facet | Deshpande, Abhishek Müller, Stefan |
| contents | The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one terminal strong component. The theorems assume the existence of a positive equilibrium and guarantee the existence of a unique positive equilibrium in every stoichiometric compatibility class.
In our work, we use the $\textit{monomial dependency}$ which extends the concept of deficiency. First, we provide a dependency one theorem for parametrized systems of polynomial equations that are essentially univariate and decomposable. As our main result, we present a corresponding theorem for mass-action systems, which permits subnetworks with arbitrary deficiency and arbitrary number of terminal strong components. Finally, to complete the picture, we derive the extended deficiency one theorem as a special case of our more general dependency one theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposable and essentially univariate mass-action systems: Extensions of the deficiency one theorem Deshpande, Abhishek Müller, Stefan Dynamical Systems Molecular Networks The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one terminal strong component. The theorems assume the existence of a positive equilibrium and guarantee the existence of a unique positive equilibrium in every stoichiometric compatibility class. In our work, we use the $\textit{monomial dependency}$ which extends the concept of deficiency. First, we provide a dependency one theorem for parametrized systems of polynomial equations that are essentially univariate and decomposable. As our main result, we present a corresponding theorem for mass-action systems, which permits subnetworks with arbitrary deficiency and arbitrary number of terminal strong components. Finally, to complete the picture, we derive the extended deficiency one theorem as a special case of our more general dependency one theorem. |
| title | Decomposable and essentially univariate mass-action systems: Extensions of the deficiency one theorem |
| topic | Dynamical Systems Molecular Networks |
| url | https://arxiv.org/abs/2502.21167 |