Math @ Duke

Publications [#243899] of Ezra Miller
Papers Published
 with Gopalkrishnan, M, A Projection Argument for Differential Inclusions, with Applications to Persistence of MassAction Kinetics,
Symmetry, Integrability and Geometry: Methods and Applications, vol. 9
(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 2019/01/23)
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
massaction 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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