On the persistence and global stability of mass-action systems

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.