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Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)
A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
Manoj Gopalkrishnana, Ezra Millerb, Anne Shiuc a School of Technology and Computer Science, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400 005, India
b Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, USA
c Department of Mathematics, University of Chicago,
5734 S. University Avenue, Chicago, IL 60637, USA
Аннотация:
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.
Ключевые слова:
differential inclusion; mass-action kinetics; reaction network; persistence; global attractor conjecture.
Поступила: 7 августа 2012 г.; в окончательном варианте 23 марта 2013 г.; опубликована 26 марта 2013 г.
Образец цитирования:
Manoj Gopalkrishnan, Ezra Miller, Anne Shiu, “A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics”, SIGMA, 9 (2013), 025, 25 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma808 https://www.mathnet.ru/rus/sigma/v9/p25
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