A geometric approach to the global attractor conjecture


Journal Article

© 2014 Society for Industrial and Applied Mathematics. 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.

Full Text

Duke Authors

Cited Authors

  • Gopalkrishnan, M; Miller, E; Shiu, A

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 13 / 2

Start / End Page

  • 758 - 797

Electronic International Standard Serial Number (EISSN)

  • 1536-0040

Digital Object Identifier (DOI)

  • 10.1137/130928170

Citation Source

  • Scopus