Mathematics > Dynamical Systems
[Submitted on 4 Aug 2012 (v1), last revised 26 Mar 2013 (this version, v5)]
Title:A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
View PDFAbstract: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.
Submission history
From: Anne Shiu [view email] [via SIGMA proxy][v1] Sat, 4 Aug 2012 01:59:59 UTC (33 KB)
[v2] Wed, 6 Feb 2013 15:23:33 UTC (43 KB)
[v3] Fri, 15 Mar 2013 13:32:30 UTC (36 KB)
[v4] Sat, 23 Mar 2013 18:00:00 UTC (36 KB)
[v5] Tue, 26 Mar 2013 06:58:20 UTC (54 KB)
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