# A geometric approach to the Global Attractor Conjecture

Source: [A geometric approach to the Global Attractor Conjecture](<https://www.sota2.com/research/paper/68fa512a1e209131ce9718df>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:16:28.658Z

Authors: Manoj Gopalkrishnan, Ezra Miller, Anne Shiu

Published: 2013-05-23T02:43:50.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1305.5303>)

[PDF](<https://arxiv.org/pdf/1305.5303.pdf>)