Publications [#221011] of Ezra Miller

Papers Accepted

1. with Manoj Gopalkrishnan and Anne Shiu, A geometric approach to the Global Attractor Conjecture, SIADS (SIAM Journal on Applied Dynamical Systems) (2013) (49 pages.) [math.DS/1305.5303]
   (last updated on 2013/12/20)

   Abstract:
   This paper introduces the class of "strongly endotactic networks", a subclass of the endotactic networks introduced by G. Craciun, F. Nazarov, and C. 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 D. F. 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.