Math @ Duke

Publications [#243899] of Ezra Miller
Papers Published
 with Gopalkrishnan, M; Miller, E; Shiu, A, A projection argument for differential inclusions, with applications to persistence of massaction kinetics,
Symmetry, Integrability and Geometry: Methods and Applications, vol. 9
(August, 2013), SIGMA (Symmetry, Integrability and Geometry: Methods and Application) (paper 025, 25 pages.) [math.DS/1208.0874], [DOI:10.3842/SIGMA.2013.025], [doi]
(last updated on 2021/05/08)
Abstract: Motivated by questions in massaction 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 lowerdimensional member of the family approaches the boundary. With this technology, we make progress on the global attractor conjecture, a central open problem concerning massaction kinetics systems. Additionally, we phrase massaction kinetics as a functor on reaction networks with variable rates.


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