The inheritance of local bifurcations in mass action networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912380205662208 |
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| author | Banaji, Murad Boros, Balázs Hofbauer, Josef |
| author_facet | Banaji, Murad Boros, Balázs Hofbauer, Josef |
| contents | We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a general transversality condition, we list some enlargements of the network which preserve its capacity for the bifurcation. These results allow us to identify bifurcations in reaction networks from examination of their subnetworks, extending and complementing previous results on the inheritance of nontrivial dynamical behaviours amongst mass action networks. A number of examples are presented to illustrate applicability of the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12897 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The inheritance of local bifurcations in mass action networks Banaji, Murad Boros, Balázs Hofbauer, Josef Dynamical Systems Classical Analysis and ODEs 34C23, 80A30, 34D15 We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a general transversality condition, we list some enlargements of the network which preserve its capacity for the bifurcation. These results allow us to identify bifurcations in reaction networks from examination of their subnetworks, extending and complementing previous results on the inheritance of nontrivial dynamical behaviours amongst mass action networks. A number of examples are presented to illustrate applicability of the results. |
| title | The inheritance of local bifurcations in mass action networks |
| topic | Dynamical Systems Classical Analysis and ODEs 34C23, 80A30, 34D15 |
| url | https://arxiv.org/abs/2312.12897 |