Name
Abstract | ||
|---|---|---|
This paper introduces the class of strongly endotactic networks, a subclass of the endotactic networks introduced by Craciun, Nazarov, and Pantea. The main result states that the global attractor conjecture holds for complex-balanced systems that are strongly endotactic: every trajectory with positive initial condition converges to the unique positive equilibrium allowed by conservation laws. This extends a recent result by Anderson for systems where the reaction diagram has only one linkage class (connected component). The results here are proved using differential inclusions, a setting that includes power-law systems. The key ideas include a perspective on reaction kinetics in terms of combinatorial geometry of reaction diagrams, a projection argument that enables analysis of a given system in terms of systems with lower dimension, and an extension of Birch's theorem, a well-known result about intersections of affine subspaces with manifolds parameterized by monomials. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/130928170 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |
Keywords | Field | DocType |
differential inclusion,mass-action kinetics,reaction network,persistence,global attractor conjecture,polytope,Birch's theorem | Attractor,Differential inclusion,Discrete geometry,Mathematical analysis,Birch's theorem,Initial value problem,Conjecture,Conservation law,Mathematics,Manifold | Journal |
Volume | Issue | ISSN |
13 | 2 | 1536-0040 |
Citations | PageRank | References |
12 | 0.94 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Manoj Gopalkrishnan | 1 | 14 | 4.56 |
| Ezra Miller | 2 | 12 | 1.62 |
| Anne Shiu | 3 | 87 | 14.47 |