Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective
Abstract Systems of differential equations with polynomial right-hand sides are very common in applications. In particular, when restricted to the positive orthant, they appear naturally (according to the law of mass-action kinetics) in ecology, population dynamics, as models of biochemical interaction networks, and models of the spread of infectious diseases. Their mathematical analysis is very challenging in general; in particular, it is very difficult to answer questions about the long-term dynamics of the variables (species) in the model, such as questions about persistence and extinction. Even if we restrict our attention to mass-action systems, these questions still remain challenging. On the other hand, if a polynomial dynamical system has a weakly reversible single linkage class (%$W\!R^1%$) realization, then its long-term dynamics is known to be remarkably robust: all the variables are persistent (i.e., no species goes extinct), irrespective of the values of the parameters in the model. Here we describe an algorithm for finding %$W\!R^1%$ realizations of polynomial dynamical systems, whenever such realizations exist..
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2023 |
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| Erschienen: |
2023 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:62 |
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| Enthalten in: |
Journal of mathematical chemistry - 62(2023), 2 vom: 30. Nov., Seite 476-501 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Craciun, Gheorghe [VerfasserIn] |
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| Links: |
Volltext [lizenzpflichtig] |
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| Anmerkungen: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| doi: |
10.1007/s10910-023-01540-1 |
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SPR054447240 |
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| 520 | |a Abstract Systems of differential equations with polynomial right-hand sides are very common in applications. In particular, when restricted to the positive orthant, they appear naturally (according to the law of mass-action kinetics) in ecology, population dynamics, as models of biochemical interaction networks, and models of the spread of infectious diseases. Their mathematical analysis is very challenging in general; in particular, it is very difficult to answer questions about the long-term dynamics of the variables (species) in the model, such as questions about persistence and extinction. Even if we restrict our attention to mass-action systems, these questions still remain challenging. On the other hand, if a polynomial dynamical system has a weakly reversible single linkage class (%$W\!R^1%$) realization, then its long-term dynamics is known to be remarkably robust: all the variables are persistent (i.e., no species goes extinct), irrespective of the values of the parameters in the model. Here we describe an algorithm for finding %$W\!R^1%$ realizations of polynomial dynamical systems, whenever such realizations exist. | ||
| 650 | 4 | |a Weakly reversible |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Single linkage class |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Realization |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Deshpande, Abhishek |4 aut | |
| 700 | 1 | |a Jin, Jiaxin |4 aut | |
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