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 –...
Збережено в:
| Дата: | 2013 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149229 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| id |
irk-123456789-149229 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1492292019-02-20T01:23:11Z A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics Gopalkrishnan, M. Miller, E. Shiu, A. 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. 2013 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149229 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Gopalkrishnan, M. Miller, E. Shiu, A. |
| spellingShingle |
Gopalkrishnan, M. Miller, E. Shiu, A. A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gopalkrishnan, M. Miller, E. Shiu, A. |
| author_sort |
Gopalkrishnan, M. |
| title |
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_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_sort |
projection argument for differential inclusions, with applications to persistence of mass-action kinetics |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149229 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT gopalkrishnanm aprojectionargumentfordifferentialinclusionswithapplicationstopersistenceofmassactionkinetics AT millere aprojectionargumentfordifferentialinclusionswithapplicationstopersistenceofmassactionkinetics AT shiua aprojectionargumentfordifferentialinclusionswithapplicationstopersistenceofmassactionkinetics AT gopalkrishnanm projectionargumentfordifferentialinclusionswithapplicationstopersistenceofmassactionkinetics AT millere projectionargumentfordifferentialinclusionswithapplicationstopersistenceofmassactionkinetics AT shiua projectionargumentfordifferentialinclusionswithapplicationstopersistenceofmassactionkinetics |
| first_indexed |
2023-05-20T17:32:17Z |
| last_indexed |
2023-05-20T17:32:17Z |
| _version_ |
1796153515979046912 |