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Publications [#243889] of Ezra Miller

Papers Accepted

  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 (2013), pp. 758-797 (49 pages.) [math.DS/1305.5303], [doi]
    (last updated on 2017/12/12)

    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.

 

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