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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2305.19410 |
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| _version_ | 1866912138160766976 |
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| author | Gutierrez, Awildo Leake, Elijah Rivas-Sobie, Caelyn Garcia, Jordy Lopez Shiu, Anne |
| author_facet | Gutierrez, Awildo Leake, Elijah Rivas-Sobie, Caelyn Garcia, Jordy Lopez Shiu, Anne |
| contents | We investigate six operations on chemical reaction networks, all of which have been proven to preserve important dynamical properties, namely, the capacity for nondegenerate multistationarity (multiple steady states) and periodic orbits. Both multistationarity and periodic orbits are properties that are known to be precluded when the deficiency (a nonnegative integer associated to a network) is zero. It is therefore natural to conjecture that the deficiency never decreases when any of the six aforementioned network operations are performed. We prove that this is indeed the case, and moreover, we characterize the numerical difference in deficiency after performing each network operation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19410 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deficiency of chemical reaction networks: The effect of operations that preserve multistationarity and periodic orbits Gutierrez, Awildo Leake, Elijah Rivas-Sobie, Caelyn Garcia, Jordy Lopez Shiu, Anne Dynamical Systems Combinatorics 37N25, 05C90, 05C76, 15A03 We investigate six operations on chemical reaction networks, all of which have been proven to preserve important dynamical properties, namely, the capacity for nondegenerate multistationarity (multiple steady states) and periodic orbits. Both multistationarity and periodic orbits are properties that are known to be precluded when the deficiency (a nonnegative integer associated to a network) is zero. It is therefore natural to conjecture that the deficiency never decreases when any of the six aforementioned network operations are performed. We prove that this is indeed the case, and moreover, we characterize the numerical difference in deficiency after performing each network operation. |
| title | Deficiency of chemical reaction networks: The effect of operations that preserve multistationarity and periodic orbits |
| topic | Dynamical Systems Combinatorics 37N25, 05C90, 05C76, 15A03 |
| url | https://arxiv.org/abs/2305.19410 |