Robust steady states in ecosystems with symmetries
Steady states of dynamical systems, whether stable or unstable, are critical for understanding future evolution. Robust steady states, ones that persist under small changes in the model parameters, are desired when modelling ecological systems, where it is common for accurate and detailed informatio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/17513758.2023.2259223 |
| _version_ | 1827362851522609152 |
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| author | Sana Jahedi Timothy Sauer James A. Yorke |
| author_facet | Sana Jahedi Timothy Sauer James A. Yorke |
| author_sort | Sana Jahedi |
| collection | DOAJ |
| description | Steady states of dynamical systems, whether stable or unstable, are critical for understanding future evolution. Robust steady states, ones that persist under small changes in the model parameters, are desired when modelling ecological systems, where it is common for accurate and detailed information on functional form and parameters to be unavailable. Previous work by Jahedi et al. [Robustness of solutions of almost every system of equations, SIAM J. Appl. Math. 82(5) (2022), pp. 1791–1807; Structured systems of nonlinear equations, SIAM J. Appl. Math. 83(4) (2023), pp. 1696–1716.] has established criteria to imply the prevalence of robust steady states for systems with minimal predetermined structure, including conventional structured systems. We review that work and extend it by allowing symmetries in the system structure, which present added obstructions to robustness. |
| first_indexed | 2024-03-08T07:36:29Z |
| format | Article |
| id | doaj.art-b6b5d4d2b4354cbe828762795173f550 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-03-08T07:36:29Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-b6b5d4d2b4354cbe828762795173f5502024-02-02T18:51:34ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662023-12-0117110.1080/17513758.2023.2259223Robust steady states in ecosystems with symmetriesSana Jahedi0Timothy Sauer1James A. Yorke2McMaster University, Hamilton, CanadaGeorge Mason University, Fairfax, VA, USAUniversity of Maryland, College Park, MD, USASteady states of dynamical systems, whether stable or unstable, are critical for understanding future evolution. Robust steady states, ones that persist under small changes in the model parameters, are desired when modelling ecological systems, where it is common for accurate and detailed information on functional form and parameters to be unavailable. Previous work by Jahedi et al. [Robustness of solutions of almost every system of equations, SIAM J. Appl. Math. 82(5) (2022), pp. 1791–1807; Structured systems of nonlinear equations, SIAM J. Appl. Math. 83(4) (2023), pp. 1696–1716.] has established criteria to imply the prevalence of robust steady states for systems with minimal predetermined structure, including conventional structured systems. We review that work and extend it by allowing symmetries in the system structure, which present added obstructions to robustness.https://www.tandfonline.com/doi/10.1080/17513758.2023.2259223Ecological modellingsteady states of dynamical systemssolutions of systems of equationssymmetric structure |
| spellingShingle | Sana Jahedi Timothy Sauer James A. Yorke Robust steady states in ecosystems with symmetries Journal of Biological Dynamics Ecological modelling steady states of dynamical systems solutions of systems of equations symmetric structure |
| title | Robust steady states in ecosystems with symmetries |
| title_full | Robust steady states in ecosystems with symmetries |
| title_fullStr | Robust steady states in ecosystems with symmetries |
| title_full_unstemmed | Robust steady states in ecosystems with symmetries |
| title_short | Robust steady states in ecosystems with symmetries |
| title_sort | robust steady states in ecosystems with symmetries |
| topic | Ecological modelling steady states of dynamical systems solutions of systems of equations symmetric structure |
| url | https://www.tandfonline.com/doi/10.1080/17513758.2023.2259223 |
| work_keys_str_mv | AT sanajahedi robuststeadystatesinecosystemswithsymmetries AT timothysauer robuststeadystatesinecosystemswithsymmetries AT jamesayorke robuststeadystatesinecosystemswithsymmetries |