The generic geometry of steady state varieties
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909042424676352 |
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| author | Feliu, Elisenda Henriksson, Oskar Pascual-Escudero, Beatriz |
| author_facet | Feliu, Elisenda Henriksson, Oskar Pascual-Escudero, Beatriz |
| contents | We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The generic geometry of steady state varieties Feliu, Elisenda Henriksson, Oskar Pascual-Escudero, Beatriz Molecular Networks Algebraic Geometry Dynamical Systems 92C42, 37N25, 14A25, 14Q30, 14P10 We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros. |
| title | The generic geometry of steady state varieties |
| topic | Molecular Networks Algebraic Geometry Dynamical Systems 92C42, 37N25, 14A25, 14Q30, 14P10 |
| url | https://arxiv.org/abs/2412.17798 |