A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
Motivated by questions in mass-action kinetics, we introduce the notion of vertexical family of differential inclusions. Defined on open hypercubes, these families are characterized by particular good behavior under projection maps. The motivating examples are certain families of reaction networks –...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2013 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149229 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics / M. Gopalkrishnan, E. Miller, A. Shiu // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709995990155264 |
|---|---|
| author | Gopalkrishnan, M. Miller, E. Shiu, A. |
| author_facet | Gopalkrishnan, M. Miller, E. Shiu, A. |
| citation_txt | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics / M. Gopalkrishnan, E. Miller, A. Shiu // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Motivated by questions in mass-action kinetics, we introduce the notion of vertexical family of differential inclusions. Defined on open hypercubes, these families are characterized by particular good behavior under projection maps. The motivating examples are certain families of reaction networks – including reversible, weakly reversible, endotactic, and strongly endotactic reaction networks – that give rise to vertexical families of mass-action differential inclusions. We prove that vertexical families are amenable to structural induction. Consequently, a trajectory of a vertexical family approaches the boundary if and only if either the trajectory approaches a vertex of the hypercube, or a trajectory in a lower-dimensional member of the family approaches the boundary. With this technology, we make progress on the global attractor conjecture, a central open problem concerning mass-action kinetics systems. Additionally, we phrase mass-action kinetics as a functor on reaction networks with variable rates.
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| first_indexed | 2025-12-07T17:21:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149229 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:21:35Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gopalkrishnan, M. Miller, E. Shiu, A. 2019-02-19T19:02:47Z 2019-02-19T19:02:47Z 2013 A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics / M. Gopalkrishnan, E. Miller, A. Shiu // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34A60; 80A30; 92C45; 37B25; 34D23; 37C10; 37C15; 92E20; 92C42; 54B30; 18B30 DOI: http://dx.doi.org/10.3842/SIGMA.2013.025 https://nasplib.isofts.kiev.ua/handle/123456789/149229 Motivated by questions in mass-action kinetics, we introduce the notion of vertexical family of differential inclusions. Defined on open hypercubes, these families are characterized by particular good behavior under projection maps. The motivating examples are certain families of reaction networks – including reversible, weakly reversible, endotactic, and strongly endotactic reaction networks – that give rise to vertexical families of mass-action differential inclusions. We prove that vertexical families are amenable to structural induction. Consequently, a trajectory of a vertexical family approaches the boundary if and only if either the trajectory approaches a vertex of the hypercube, or a trajectory in a lower-dimensional member of the family approaches the boundary. With this technology, we make progress on the global attractor conjecture, a central open problem concerning mass-action kinetics systems. Additionally, we phrase mass-action kinetics as a functor on reaction networks with variable rates. MG was supported by a Ramanujan fellowship from the Department of Science and Technology,
 India, and, during a semester-long stay at Duke University, by the Duke MathBio RTG grant
 NSF DMS-0943760. EM had support from NSF grant DMS-1001437. AS was supported by an
 NSF postdoctoral fellowship DMS-1004380. The authors thank David F. Anderson, Gheorghe
 Craciun, and Casian Pantea for helpful discussions, and Duke University where many of the
 conversations occurred. The authors also thank the two referees, whose perceptive and insightful
 comments improved this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics Article published earlier |
| spellingShingle | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics Gopalkrishnan, M. Miller, E. Shiu, A. |
| title | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics |
| title_full | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics |
| title_fullStr | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics |
| title_full_unstemmed | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics |
| title_short | A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics |
| title_sort | projection argument for differential inclusions, with applications to persistence of mass-action kinetics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149229 |
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