# On the persistence and global stability of mass-action systems

Source: [On the persistence and global stability of mass-action systems](<https://www.sota2.com/research/paper/68fa4f9c1e209131ce964cf4>)

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

Data updated: 2025-10-25T10:24:42.478Z

Authors: Casian Pantea

Published: 2011-03-03T04:00:22.000Z

## Abstract

This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction Network Theory, the Persistence Conjecture and the Global Attractor Conjecture. We study the persistence of a large class of networks called lower-endotactic and in particular, we show that in weakly reversible mass-action systems with two-dimensional stoichiometric subspace all bounded trajectories are persistent. Moreover, we use these ideas to show that the Global Attractor Conjecture is true for systems with three-dimensional stoichiometric subspace.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1103.0603>)

[PDF](<https://arxiv.org/pdf/1103.0603.pdf>)