A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
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| Creator |
Gopalkrishnan, M.
Miller, E. Shiu, A. |
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| 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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| Date |
2019-02-19T19:02:47Z
2019-02-19T19:02:47Z 2013 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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