On the persistence and global stability of mass-action systems

TL;DR

This paper advances understanding of chemical reaction systems by proving persistence and global stability for specific classes of mass-action systems, addressing key open conjectures in the field.

Contribution

It proves persistence for weakly reversible systems with two-dimensional stoichiometry and confirms the Global Attractor Conjecture for three-dimensional cases.

Findings

Persistence of bounded trajectories in certain networks

Validation of the Global Attractor Conjecture in 3D systems

Progress on long-standing open problems in Chemical Reaction Network Theory

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.