Publications [#243889] of Ezra Miller

Papers Published

1. with Gopalkrishnan, M; Miller, E; Shiu, A, A geometric approach to the global attractor conjecture, SIAM Journal on Applied Dynamical Systems, vol. 13 no. 2 (January, 2014), pp. 758-797, Society for Industrial & Applied Mathematics (SIAM) (49 pages.) [math.DS/1305.5303], [doi]
   (last updated on 2026/01/14)

   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.